Internally, repeaters consist of at least two radios. The MXT500 is only one. Depending upon how you built everything else in the system out, including whether you used one antenna or two, whether you were using a duplexer, and whether or not you built custom circuitry to allow you to integrate a mic while the two radios are interconnected, then perhaps.
The Wouxon KG-1000G is the only Part 95e radio I know of that is built to be used as a component of a custom limited-use repeater build, and OffRoaderX did it. It has the internal circuitry necessary for interconnecting two like models, and has modes for changing the radios behavior to operate as components of a repeater system. If using this model, yes you could use its mic to transmit while the radio is configured as a repeater, but only on the repeater Tx frequency. However, to use the radios for general comms you would need to be using separate antennas and you would need to switch the radios back into standard mode.
My advice, if you want a repeater, buy and put up a purpose built repeater.
WRPD571 got a reaction from mbrun in Repeater use