That's one of good receivers i hear about. 3D and 4K upscaling. Secure for future!!!
Yes, it does go with AM10 series. One of very good combinations. Do check here, if you have not seen them.
AV receivers from 4 to 8 ohms are supported. (and 100-200w per channel) So your NR 636 should fit in it. (Even AM6 supports it) Do check the manual of bose. It's clear there. If you cannot get it, let me know. I shall send you the manual.