One point worth considering is that "I'll check my schedule" implies that the event being proposed isn't very high up their priority list... so far down their priority list that they can't remember of all the other things they'd consider higher priority. If it was clashing with something REALLY high up their priority list, such as partner's birthday party they'd been planning for weeks, they'd be able to give a straight "no" pretty quickly... and if YOUR event was pretty high up their priority list (so they'd re-arrange their schedule to attend) they'd be able to give a "yes" pretty quickly. —
Steve 6 secs ago