I actively operate and program several handheld Kenwood (TK-370G/372G) radios. My experience has been that in the Type 1 range (450-470 MHz) these units will take the programming and operate outside the rated band spread. You can push it to at least 8 MHz above and below the rated frequency range. Ham repeaters in the lower portion of the 440 MHz band should not pose a problem. Maybe at 10 MHz away from the rated range you may experience some degradation on transmit and receive, but your mileage may vary.
I have programmed my business, amateur, GMRS, public safety frequencies with this model without any issues. Although discontinued, the 70 series portable provided owners with the best value. The alpha numeric display is robust and the TK-372G models can be forced to take the programming from the sister radio the TK-370G to fool it from a 32 channel model to a 128 channel model.