If I were choosing a PSU I would choose one with at least 28 amps on the 3.3 rail, but that effects the RAM primarily. Your PSU has only 24. You have dual 12v rails with 22 x 22 amps. You should be good. I have a 7900GTO running on similar specs as yours. My Thermaltake has 4 x 12v rails though.
The answer is no, even if it works in the short term it is not appropriate for longer term use. Only you can decide if it is worth the gamble to use it for the time being, getting more value of the price paid. With occasional stress only and good case cooling, it may do the job for a reasonable amount of time. With constant high load and poor cooling it might fail in months.
Better question is, if you are a gamer with a tendency to buy higher powered video cards, why did you buy a generic PSU? On most budget PSU you can't add up current on each separate rail, if it's 12V1 @ 22A and 12V2 @ 22A, it certainly isn't 44A total. Probably closer to 25A peak (at 25C temp), which could run the system, but really if you had another system you might reuse that PSU in, it would be best to replace it rather than burning the candle at both ends to wear it out faster.
Also, please post appropriate titles for your thread, "quick question" is the opposite of an appropriate title since most threads start out with a quick question but the title is meant to describe the TOPIC of the thread. Thank you.
ha...sry...was in a rush..had to go out..so sry about the title...and about the psu, it looked good enough to power my current system, and i thought it could power my future system. I guess not, so, im guessing get a new power supply to make sure of that?
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