I could see this being really good or really bad.I'm not a Sun Scorpio, but I am a Venus Scorpio. I have a good Venus Virgo friend. (We are both Libra suns). I'd say that we balance each other out. She tends to be service-oriented, sees the good in people, can be self-critical, wants things to be beautiful and pure. I feel like she helps me to see that people can be good, and that she helps tone down my hubris just by my being around her: I see what a giving and caring person she is and it makes me want to be a better person. The only tension is that I feel like I have to "behave myself" (as in, have to censor myself a bit, as I tend to have a much darker sense of humor and things like that), but, on the other hand, I do feel like it raises me to a higher standard. I actually told her that once, and she told me that (a) I don't have to do that and (b) that she feels a need to accept reality more and see things as they are, to acknowledge the dark side of life, and that I help her do that. So, again, balance.
I would say that one big source of tension would be Virgo's criticism. Even if it's a well-intentioned Virgo who is just trying to help, it can get VERY annoying very quickly to be nit-picked all of the time. On the other hand, though, Virgos can help you raise your own bar. So, I'd say that both sides would have to work together: Virgos can learn to give constructive criticism tactfully and when appropriate, and hold back when it's really not appropriate to criticize. Scorpio can put aside suspicions and at least consider Virgo's opinion sometimes.
The other issue is that Virgos/Virgo influenced people tend to sanitize things, whereas Scorpio doesn't. This, as I said, came up with my Venus Virgo friend and myself. It also was an issue with me and my grandmother, who was likely a sun Virgo (she was born the day it changed from Leo to Virgo and we don't have her birth time; she's deceased so I can't ask) and had several other planets in Virgo. I've noticed that a lot of Virgos get more easily offended by things like swearing than a lot of other signs. However, as I also pointed out, this can bring both to a point of balance: Virgo can accept that the world isn't always clean and decent and Scorpio can tone things down a bit.
As for sex drive, I don't know about that, as I've never slept with a Virgo or have been romantically tangled with one, but I would say that many Virgo-influenced people whom I've known who've talked to me about those things seem to be cautious and careful about sex. Personally, I would not consider a lower sex drive to be a 'problem' necessarily: quality, to me, is more important than quantity when it comes to pretty much anything. I'd also say that sex drive discrepancy is not a sign-specific problem: this can be a problem between people of any two signs/placements. With any relationship, some compromise is necessary.