Nevermind the short answer, the real answer is Yes.
Photoshop etc all use 2d graphics only. Your onboard graphics card is more than enough.
Your photos are 2D, and any manipulations done on them are just mathematics for 2d manipulation. The common graphics cards finish 2D graphics display in a snap. They are more expensive because the cards boasts of superior 3d accelerators: They accelerate drawing of 3d graphics. They can't do nuts for 2D graphics (think your processor)
You will not see ANY difference between a $700 gaming graphics card and onboard graphics card.
If you want to listen to the computer illiterate, at least take a moment to consider the system requirements for photoshop:
http://www.adobe.com/products/photoshop/photoshop/systemreqs/
They stated the minimum hardware requirements (pentium, centrino or better), but they only require a 16 bit graphics card. Makes you wonder if the people who created photoshop know what they're talking about, doesn't it?
No way man. That's a negative.
No calculations are done using graphics cards for simple 2d graphics (think photoshop).
Onboard graphics cards may suck at 3d acceleration, but they're no different from a $700 graphics card for normal display.