could it output 4W (or more) even if the signal is clipped/saturated

As I've stated several times, NO.

 

A maximally clipped waveform is a square wave, and it has twice the power of an unclipped sine wave but...
The extra power is in harmonics. It has no more power at the fundamental frequency than the maximum unclipped sine wave.

You are in the realm of what my wife calls magical thinking if you think you can get useful power out of that signal amplifier.

Bob

i really appreciate your knowledge, i just find that with the 20W consumption that it could only output 13mW is too much a loss, it is an efficiency question, i am not looking for any useful power or signal at all, i just need to know, what wattage it could put out (all inclusive of all broadband harmonics), it is more of a structural efficiency question, what power can it possibly use to convert the input RF into RF and into heat from the 20W consumption (irrespective of signal usefulness)?

 

amp specifications:

• Input Frequency Range: 40 ~ 860 MHz
• Output Max Level: 60 dBmV
• Gain: 50 dB maximum
• Gain Control Range: 0 ~ -18 dB adjustable
• Tilt Control Range: 0 ~ -16 dB adjustable
• Noise Figure: 7 dB
• Flatness: +/- 2 dB
• Input Return Loss: >13dB
• Output Return Loss: >14dB
• Input/ Output Impedance: 75 ohm
• Input/ Output Test Port: - 20 dB
• Dimension: 498mm (W) x 360mm (D) x 280mm (H)
• Connectors: All F type female connectors
• Internal AC Fuse: 1 Amp
• Operating Temperature: 0 ~ 50 degree C
• Power Supply: AC 110V +-10%
• Power Consumption: 20W

 

A a voltage amplifier into a dummy load would show transmitter power.
As an antenna the signal strength is poor.
The radiating charecteristics are shown in a polar diagram.
As the antenna is broad banded the Q is reduced.
Lowering the Q of the antenna allows distribution over broader range.
However getting the VSWR down is the ticket.
https://www.antenna-theory.com/definitions/vswr.php