Sure, if that's what they both enjoy doing, then it's a great idea. The most important part of a relationship is doing things together, so why not let that thing be gaming? I only a bit of gaming every once in a while, and I'm sure a lot of girls do, so I wouldn't mind playing with my boyfriend. As long as he can deal with my grumpiness when the "console" doesn't do what I want it to do
I do think it's a good idea! It's silly, but the fact that my wife was so good at Starcraft was one of the things that attracted me to her.
After we married, she got really into WoW, raiding extensively. It actually started to put a strain on our relationship. A few months go by, and I really get into WoW raiding too. Raiding together was much better on our relationship - we were partners again. Time goes by, and I stayed active in the guild, but she cut back. Again our relationship suffered... so there's definitely a balance there.
When we find a game that we can enjoy jointly, it becomes a bonding experience. I wrote a hub on this subject <link snipped, no self promotion.>
I think any activity a couple does together can be a great thing, as long as both enjoy it. My husband and I used to play video games together a lot. Lately we've seemed to lose interest. We usually game more in the winter when the weather is bad and there isn't too much to do outside.
It's a good idea, though video games tend to offer more options and debates, RPGs the most. For example, my lover and I play World of Warcraft together, and whenever we make a new character said lover always chooses Blood Elves. She knows I despise them, though I force myself into making a new character of that race just for her.
So doing things together is good, but depending on what it is will vary. I'm very happy with my relationship as things are going steady and smooth. But whenever it comes to gaming, there tends to be some disagreement.