Google does in fact index https pages, this can be verified by doing a search for inurl:https and most of the results you find will be to secured pages. I am not sure about other search engines, and I have no idea how this might affect crawl frequency or ranking. Based on rumors I have heard, it may have a tiny benefit because using encryption requires a digital signature, which implies trust.

__________________
The best way to learn anything, is to question everything.