Returning back to your original question and not the folks motivated to keep you purchasing :
Yes your 350W will work fine, the reason why AMD recommends 400W is that they dont want people filing tech support tickets on there help desk system.
AMD 7750 (please grab the GDDR5 and not GDDR3 version) consumes 55w, your CPU :
http://ark.intel.com/products/37006/
Consumes according to intel 25W
so even with RAM and HDD (~15W) you wont be above 100W
So go for it and best rest assured