Will this High Frequency AC Signal Generator Circuit work?
You have a push-pull configuration. I assume, you will turn: on positive->off positive->dead time->on negative->dead time-> ...repeat.

At 10kHZ with duty ratio 50:50, ommiting the dead time you get a voltage integral of 165uVs for each half cycle. So too big for a transformer that accepts 30uVS. You may not be able to work at lower frequency.