[QUOTE=sdsearch;Also, do you get HH stay credit when using AA miles to book a HH hotel? With HH giving stay credit for award stays (including points+cash), some people need their award stays to count for HH stays in order to (re)qualify for the HH status they want.[/QUOTE]

No credit when booking through a third party site.
If you want credit you would have to book directly through hilton.