If the PSU isn't powerfull enough, it either won't start at all or will wear otu quickly but I don't think it will damage the rest of your system ( unless it catches fire, in which case it could even damage your hosue ).
That's one reason I only by the case and PSU seperately...been bitten one with the combo thing, and I won't do it again. But I guess that's how you learn sometimes.
if i were you i would look at the pther components on the power supply it is just like one or two hard drives and the cpu cooler it should be fine. i used to run 3 hard drives as well as 8 case fans on my old 300w generic. so one should be ok. if i were yo i would upgrade to a bigger one such as an enermax or i have also found that the aopen 350w or higher is usually stable enough. just go for it a new power supply dont cost jack and it easy to install.