No it won't damage the radio. As long as the radio antenna terminal sees 50 ohms and the input to the amplifier is 50 ohms, you're ok.
However.........
The amplifier is tuned for 150.?? and above. Using the amp outside the MFR spec'd freq. range may induce some dirty harmonics into the airwaves. You could possibly be transmitting a harmonic on some freq. where it's not supposed to be and be picked up by someone else on another frequency and contexted as intereference, have them come a-looking. Lucy.....you got some 'splaining to do.
It is really close to the upper end of the ham bands, and probably won't do much harm, but if you know someone with an RF specturm analyzer, like maybe one of the more seasoned ham radio professionals in your area may be able to "sweep it" for you to make sure everything's on the up and up.
Otherwise, a great power booster for an HT as long as your batteries can hold out. keep the transmissions short!!
Good Luck.
rcvmo