This system is from hp, and the power just seems a little too low. 460watt power ati hd4650 1g 6 gig ddr3 ram 3 dimms i-7 860 processor 640 gig 7200 rpm sata hardrive
Will this run out of the box without power problems and/or putting too much stress on the computer, or will i have to upgrade it so something stronger?
You can be 100% sure that if HP sells this directly, the power supply will be enough for the system plus at least 10% headroom. It's been engineered and tested FAR more than any homebuilt system. It may not have enough power for high draw upgrades though but HP (or anyone else) can't and won't account for that.
The answer to your question is yes. The official requirement for the ATI Radeon 4650 video card is a 400 watt power supply. That recommendation is for an entire pc system. You should not have any problems.