As far as I can tell without the schematic of the mic, it will not work. The input of the uBitx has approximately 5 K ohms for the bias of the electret element. If the current draw of the mic is 5 ma, then the drop across that resistor would be 25 volts. At most the supplied voltage is 12 volts (13.8 with a "normal" ham supply). Not enough to run the mic. You would need to drop the resistor in the uBiTx mic circuit (R60) to 680 ohms That would give a drop of (680+220)*.005=4.5 volts. That leaves 7.5 volts for the mic. NOTE: there is a 220 ohm resistor ahead of R60.
The PTT line on the uBiTx is a direct input on the Nano, so the 2 ma max draw should not be an issue. If there is an issue, a pull-up resistor (2.2 K) should fix it.
Please double-check the above before you implement it. My recommendation is to go with another solution like a 9 volt battery in the mic or wire a separate supply at the mic connector in the uBiTx. This will depend on if you want to use an electret without a built-in amp in addition to the amplified one. If you are going to dedicate the mic and rig together, then swap the resistor after you do more verification.
Just suggestions. The short answer is that it will not work.