Don't count on Hosts getting a resort fee waved. Probably depends on where, but don't count on it.
Pay attention to offer specifications. If free nights are Sunday through Thursday, but you want to stay, say W,Th, and Friday night, and are willing to pay for Friday night, count on paying resort fee (and taxes) for all nights, even the free ones. Talk about a rip off. In fact, don't do it.
Even if you have a Host, but a mailed offer limits your free nights (and no resort fee) to Sunday through Thursday, or to a certain number (e.g. three free nights) ask the Host BEFORE you book if he can comp the extra night(s). In that case, if he does comp the extra, the resort fee might be waved (not via the generosity of the Host but via the electronic comping system as he puts it in); but clarify that before deciding.