Hi Spoonhead98,
I (personally) would not take a chance on using the stock cooler for a 100W AMD CPU. If you research this issue, you will find others that have complained about the stock cooler noise and some have also complained about overheating as well (when using the stock cooler). In addition, if you intend to do some gaming, that could affect your stock cooling capabilities as well.
Let me just throw in my preference for an alternative for you to consider. Specifically, I like the Intel I3-4130 over the above. Why? Because it actually benchmarks higher than the above and this 54w CPU will run just fine with the stock cooler (included).
Yes, I know the I3-4130 only has 2 cores but it is still faster than the other CPU in single-threaded operations (which is an important part of everyday general computing IMHO). So, if you consider the total cost of the AMD + after-market cooler with the base cost of the I3-4130, it is about the same. BTW, You'd also save a few bucks on electricity as well (now I'm really splitting hairs). Anyway, all just food for though so good luck with your final build. Here's a benchmark compare of the two CPUs:
UPDATE: My response is/was not in response to alphanumerics post. I did not realize we were posting simultaneously. However, since he is using the stock coolers on similar AMD CPUs, his advice is more appropriate, but I doubt he is a gamer, so please take that into consideration as well. I still prefer an Intel solution myself. Good luck.