im using a gtx 650 on a hp stock 320w psu and its working fine. No sounds smoke or anything. i'm playing all games on high ultra etc like bf4 crysis, for about 4 days and on. so can i still still go on like this for a week.
Should be fine for a short period but a stronger replacement should be installed as soon as is reasonably possible.
Not sure of HP quality, but many OEMs use cheap units which often lack the failsafe protection found in more expensive parts.
When they fail they can, in some circumstances, damage other parts of the system (CPU, motherboard etc).