For the GPU your PSU should be fine. For a single card configuration you need at least a 450 W PSU with a current rating of at least 24 Amperes on the +12V. As for the rest of your computer... if you don't have to much other hardware and power drawing devices you should be fine.
I've just read a review for GX 750 and it is quite disappointing. With yours as it smaller sibling, I'd say it would also contain the same components as the GX 750 and only differ in capacity. I would not be keen towards running your PSU at greater loads. But hey, I'm not the power guru so someone might be able to say something different about power consumption of 2 5770s.
I also have 2 5770's in CF running on top of HX620 and they're fine. Not to mention that hardwaresecrets tested this PSU to run beyond its rated power (~700w).
I think it would be fine at running a single 5770. Overclocking? You can but I'm not sure about the mobo's heat dissipating capability to say if it is good or not. Get a decent CPU cooler if your planning to do so.