I would really recommend you have an extra back fan and an intake fan in the front to ensure proper cooling and air flow. The PSU might not be enough. What kind of system are you running?
Yes then back exhaust IS needed. Like i mentioned proper air flow is the key element to prevent overheating. I don't think you want something overheating in a high end gaming system. If you think its going to make too much noise get some 120mm fans.
PSUs generally have only the cooling that they need to cool the power supply itself off (and maybe a small amount of heat coming from the inside of the case), so you should definitely get a good fan for exhausting from your case.
Most PSU's have fan(s) that dont push much air, and are only powerful enough to keep the PSU cool.
If you have any modern computer, especially a gaming computer with a dedicatd video card, it's highly recommended to have at least one additional exhaust fan.