There are worse things than the stock cooler. It may be ok as long as you never do anything to really stress the CPU.
But if you are doing any heavy computing (gaming, or folding, for example) you will find that the CPU will throttle itself down to reduce heat buildup, and there is a chance of thermal damage and in the long run there is a risk that you will reduce the lifespan of the CPU.
If all you can afford at the moment is the stock cooler, then run with it, you will be ok. But look into saving up for an aftermarket cooler. Tom's Hardware has lots of articles to read up on that will help you learn about them.