Yes. Additionally, the fact you would be using a Q6600 limits your overall system performance because of the features of the motherboards that support that processor. I don't think it would be a major bottleneck in all situations, but definitely present.
If you are building a new system in stages, and have a new processor, mobo, ram planned for later, you could get by pairing up a Q6600 with a 970 or 980, but in some more processor intensive games, you will be missing out on a decent chunk of performance. I don't know of anyone currently using this setup, but I suspect its certainly playable and will work just fine with some tweaking of game settings. Some games may max out just fine, other more complex titles might choke up a bit. It might be hit or miss with some AAA titles, but that's what settings are for.
All in all, nobody would ever say that its a good pairing. If you are looking at upgrading cpu/mobo later, then I'd consider the least expensive graphics option, like a 750ti or a gtx 960 for gaming at 1080p, save up, and do a full rebuild later this year, whenever AMD drops the 390x and nvidia inevitably fires back would be a great time for some shopping I suspect.