Can the Radeon HD3200 run 1600x900 resolution?

Sure

Yes. This info's likely easily found by Googling or at AMD/ATI's site.

It won't game well, but all graphics solutions are roughly the same for basic tasks (not counting special things like Aero support which the HD3200 does support.

Yeah, it will definitely support the resolution but gaming even at much lower resolutions won't be very good at all except on games more than a few years old.