My friend got some filthy used brass for his 50BMG. He tried an ultrasonic cleaner at work and didn't really get good results.
The standard tumbler/media method was much better. I don't know how powerful yours would be for $29.
I had the same thought, and contacted Brownell's about it. They said that the ultra-sonic cleaners will clean the brass down to bare metal, removing carbon, dirt, primer residue etc. but that it will not remove stains. In other words, the brass will be clean, just won't be bright with a polished look.
One other thing - don't use a cleaning medium with any ammonia in it.
If it's down to bare metal then what is the stain?
I saw my friends after a good hour, and it wasn't just stained, it simply wasn't getting clean.
Since you already ordered it, let us know if it works.