No, nein, absolutely nyet! I mean, would you do that if you traveled anywhere else? Then nothing should change here either.
Besides the fact that they can be drunk, especially if they're in a full-body costume or wearing a lot of make-up, they also have veeery flexible pricing policies. Which means that they don't tell you how much it costs in the beginning and then, after you've already taken your pictures, charge whatever they feel like would be the fair price for you in particular. Meaning that, as a foreigner, you WILL get ripped off. The only question is by how much.
Every single time you meet one of them next to Red Square they start with the exact same question, 'Hello, my friend! Where are you from?' And it is absolutely not because they actually care where you from. By no means should you expect any small conversation to be initiated by them after your response. They won't tell how much they love your cuisine or about that last time they traveled there. No.
The next phrase right after, 'Where are you from?' is always, 'Great! Let's take a group photo!' And the only reason they ask about your country is to try to figure out the perfect sum to charge you in the end. Which is the maximally high price that, they think, it won't kill you to pay, and yet not high enough to make you angry.
Very important distinction there. 'Not to make you angry' doesn't mean not to make you irritated or deeply upset about how high it is. Those things are absolutely fine with them. Preserving good karma is not their first priority there. As long as you don't feel angry enough to punch them in their dressed up faces or run away and call the cops, it's all a successfully set price.
Just look at them! Those are not smiling faces. Those are just covers to go deep inside themselves in the meantime and start calculating. 'Alright, they're from Brazil. What's Brazil's GDP, income per capita, political situation at the moment? What's my personal experience of trying to rip off Brazilian people so far, how many stars does their hotel have, does his girlfriend have natural tits or can they afford plastic surgery?' I'm sure it's a very deep computational process there.
And here are the approximate prices their charge people from different countries based on my personal experience:
Russian people - 200-300 RUB per group
Developing nations and Eastern Europe - 500-800 RUB per group
Western Europe and some English-speaking nations - 800-1000 RUB per group
The US or UK - 1000 RUB per person
Alternatively, for US people it can be 1000 RUB for every dressed up person in the picture instead of every tourist from your group, which there will be a lot the moment you start taking those photos. We once took a couple of pictures with just 2 guys. They said, 'Oh come on, take more'. And the more we were taking the more people started appearing in the frame. First, it was just Lenin and Stalin, 2 minutes later there was the full gang with Peter the Great, Catherine the Great, Elizabeth... or at least I thought she was Elizabeth. She might've been just a random woman attracted by the smell of money at that point.
In the end, they tried to charge us around 5000-6000 RUB and were very loudly arguing that it's a normal price, and that everybody pays that. My group turned out to be a bit more generous than I expected and decided to give 1000 RUB for all of them. They made a couple of more incoherent noises, but eventually walked away.
And that was a relatively peacefully resolved situation. They can be much more irritating than that and start following you for half a mile nagging about how you should've paid more along the way.
If something like that happens, please, feel free to find any nearest police officer (preferably with 'Tourist Police' written on his upper arm) and ask him to resolve the situation. Which is one of the few times when it would be really advisable to do so. As it won't really require almost any conversation with the police itself. Just mentioning it or intending to approach an officer would likely set everyone around you running. Note that talking to police and trying to explain any other complex issue or emergency might result in a lot of unnecessary tedium with no or dubious results. But in this case should work absolutely fine.
There are not that many things on this planet that you can be certain of 100%. Which makes those impersonating people around Red Square somewhat exceptional. Because all of our interactions with them over the last 7 years of me doing these walking tours ended up feeling in one or another way wrong or leaving a bad aftertaste for a couple of hours literally 100% of the time.
So no, it is absolutely not advisable to take pictures with any of the impersonators around Red Square or anywhere else!
But if you feel the urge to throw away 1000 RUB or more anyway, consider those two options that would make your expense a bit more worthwhile.
First, occasionally, there's a guy next to Red Square's entrance impersonating Putin. There are many of them dressed as Lenin, Stalin or Nicholas II. But there's only one that tries to pull off Putin, or at least, only one that actually looks the part:
From certain angles, especially. The nose is a bit too wide, but the rest is there. He might try to charge up to 2000 RUB, which would be totally insane. Use your negotiating skills and bring it down to at least 1000 RUB. And then at least you'll know that you've spent them on something more or less rare. I've seen many wax figures of Vladimir that looked less convincing than that guy.
And second, if you're determined to do it, at least add some imagination and set the pictures in unusual ways. For example, take a photo with both Nicholas II and Lenin. Or even better, tell Lenin to make a finger gun and point it against Nicholas' head while you're standing in the middle of them.
There used to be a bunch of Disney and Marvel character impersonators as well at some point. Not in recent years, unfortunately. But if you happen to see them return one day, don't miss a chance of taking a picture with Stalin on one side and Spider-man in a very cheap, self-made costume on the other. That's a combination that you won't see anywhere else in the world. I guarantee it ;)
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