Theoretically you could do this, at the expense of causing some noise on the channel you're transmitting on.
If you have some kind of signaling, i.e. MDC, DTMF, etc., enabled in your radio, you could set your radio to pre-PTT identify (send a data burst with your MDC ID or DTMF ID), and set your radio to generate a "sidetone" while it's transmitting the PTT-ID. That way, your radio will give you a tone while you're first pressing the Push To Talk. The downside, as I said, is, you're sending a squawk or quack of noise at the beginning of each transmission, which could get annoying to the other users of the radio system.
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--j.
VE6SRT
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