The number of monitors doesn't effect power consumption. It will likely depend on the power supply quality, but probably. I assume you mean the 7750, wasn't aware of a 7570 existing yet; either case, the answer is yeah probably, slot powered cards are limited to 75W.
If you already have the PSU, it will probably work. If you are buying the PSU, I would go a little bigger unless you are sure you are buying a good quality PSU; the overwhelming majority of aftermarket 300W PSUs are absolute garbage that shouldn't go in a computer.
If you are in the states, Corsair CX430 is available for 40$ right now on newegg.
Thanks for the info, the 7570 is an OEM from HP, the reason for my question is I bought two computers with this vidieo card, one has a 400W supply while the other has a 300W. the larger one hooked up and ran with dual monitors without issue, the other would not detect the 2nd monitor at all. I have resolved through proper cableing but i was fishing for reasons, thanks again though, good info.