Awesome Miner doesn't have this feature right now, becuase the software was originally not optimized for small scale mining on a single gaming computer where you want to start and stop the mining depending on computer use. This is a feature that could be supported, so I will make a note of this request and add it in future versions.
I would love this feature as well - I use AM for a larger mining operation at my business as well as on my home gaming PC's to mine in their free time, there is no easy way to get the PC to STOP mining using Scheduled Tasks (starting is easy), so having this built-in would be a godsend.