Yes, you'd be surprised. I had many friends, all vulnerable-looking 23 year old girls in towering heels and they used this "ride from a stranger" concept every single day for years. Believe me, I was shocked and apprehensive and my Mom was convinced I'd be murdered but it was shockingly safe and accepted. I do speak halfway decent Russian, and would certainly have been harder without it. Which is why I like the idea of this app, as it solves one of the problems. (Edit: I guess it doesn't really solve the language barrier, as it appears to be a Telegram app that likely involves some chatting to negotiate.)
That said, on my last visit, I used Uber many times, as it's incredibly cheap and requires no negotiation. But don't be in a hurry. The horrible traffic and very wide, divided streets of Moscow make it particularly challenging to navigate to a passenger's precise location, so it can be an extremely long wait even when free a vehicle is very close geographically. Perhaps LibreTaxi would help solve that by lowering the barrier to entry and drastically improving the number of cars available.