Yes you can. I've used the INT/SQW alarm output of a DS3231 RTC, which is open drain, to turn on a P-channel mosfet. But you do need the pullup resistor so the gate never floats. I used 100K, but this was just a low-current power switch, so there were no real thermal considerations. I guess in theory it could also work with an N-channel mosfet. I feel less comfortable about that, but haven't really thought it through.
They do make comparators with push/pull outputs, which would eliminate the need for the resistor, but I don't think they are common.