Yes, a ground plane antenna has a low feed-point impedance because it is fed at a current loop, and that's because the antenna is a 1/4 wave length, or some odd multiple of 1/4 wave length.
A J-pole is an end-fed 1/2 wave length antenna, making its input impedance and its radiation resistance, very high, but to make it work with 50 Ohm coax, it's fed by a 1/4 wave, balanced feedline which acts as a transformer of 50 Ohms to approximately 2500+ Ohms needed to feed the end of a 1/2 wave antenna.
The problem with any 1/4 wave/ground plane antenna mounted near the ground, is that the current loop (where most of the antenna's energy is coming from), is at ground level, and coupling to the ground plane and Earth in many places except rocky and desert areas; that, with a low radiation resistance, makes any ground-mounted ground plane antenna, fairly inefficient. A half wave antenna places the current loop away from the feed-point, and further away from the ground if the antenna is near the ground, and it doesn't need any ground plane for impedance purposes, further lowering ground losses.
Can inefficient antennas transmit and receive? Absolutely!