HD 7850 2GB is good, a little faster than the GTX 650 Ti boost.
Recommendations from AMD and Nvidia have to cover a wide range of CPUs and power supplies so they are conservative.
Your system needs at least 309W (25.75A) on the +12V rail.
Your power supply as two +12V rails, each rated at 18A.
This should be plenty.
This card requires two 6-pin PCI-E connectors.
Your power supply only has one.
Because you appear to have enough power available, you could use an adapter.
This however will require two available molex power connectors for the adapter and the supply only has one.
The card may or may not come with one of these adapters.
Short answer, you power supply is probably OK but there are a few maybes in there.
Trying it shouldn't hurt anything, but make sure all the cables are correct before powering it on.
Consider the following as alternatives:
XFX Pro 550 (very good quality 80 plus bronze rated unit, manufactured by Seasonic)
Seasonic G 450 (very good quality 80 plus gold rated unit)
Seasonic S12II 430 (very good quality 80 plus bronze rated unit)
Corsair CX 500 (not as good as the units above, but still 80 plus bronze rated and good quality for a budget supply)