As a general rule, what happens when you do this is to make the relay "chatter" or buzz.
When the relay closes, it cuts off the RF drive from the radio to the keying circuit. The relay will "click" and remain energized only until the contacts change over. This removes the radio's drive RF from the RF sensing circuit, because it was traveling through the relay's receive side. This causes the relay to drop back to receive mode. But not for long, because this reconnects the radio's RF through the relay's standby side to the sensing circuit and the cycle repeats. Migh buzz, might "chatter" several times a second.
Can't see how the amplifier would be damaged this way. The radio might not be as forgiving.
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