Yes, it is impedance ratio between antenna & system (receiver/coax/amplifier) which determines what fraction of the signal picked by antenna will be transferred to the receiver. Maximum signal transfer takes place when impedance of antenna = impedance of system. Under this condition SWR=1. Actually SWR is an indicator of signal transfer & impedance matching. Higher the SWR, higher the mismatch and lower the signal transfer. SWR 1.5 or less is considered decent as this is the range where major portion of signal transferes to the receiver.
Using a high INPUT impedance amplifier with a high impedance antenna will help, provided OUTPUT impedance of amplifier is 75 ohms and matches the 75 or 50 ohm coax/receiver.
Even using a normal sattelite amplifier (having 75 ohm input & 75 ohms output impedance), with a high impedance antenna also helps. Due to impedance mismatch between antenna and amplifier, the antenna transfers same reduced amount of signal to amplifier as it transferes to the coax/receiver without amplifier. The amplifier’s large gain boosts the reduced input signal to even higher than the full output signal of antenna. Since amplifier & coax/receiver are impedance matched (i.e. all are 75 ohms), maximum signal transfer takes place betwee amplifier and receiver. The receiver as a result gets signal even higher than maximum signal of the antenna.
I have tested this with Franklin antenna WITHOUT the impedance matching stub (i.e. the stub in the middle to which coax is connected).
Franklin without impedance matching stub is a high impedance antenna, about 400 to 600 ohms. This is a gross mismatch with 75 ohms coax/receiver. Without amplifier & 12 ft coax, It gave me max range below 100 nm. With an amplifier & 12 ft coax, its range jumped to over 200nm, and number of planes more than doubled.