Is it possible to have the NRF24 module on an Arduino Mini transmitting to an NRF24 with SMA antenna on a Mega? In that case, would the antenna on the Mega help pickup the signal of the transmitting Arduino Mini?
Yes, and yes.
A module without an antenna is exactly the same as a module with an antenna, it's just that the antenna is part of the PCB. Yes, the module with the antenna will have more sensitivity (able to receive fainter signals) as well as more transmitting power.
The same is true of the modules with the power amplifier. They again have even more sensitivity and transmitting power.
It is quite common to have a single powerful transceiver with power amplifier and antenna as a base station and then smaller modules as the remote slave devices. Especially if you couple the base station with a suitable parabolic or uni-directional high gain antenna to point directly at where the slave devices are.