I'll just share my experience with doing exactly what you mention. "Before" when I performed a live power transfer, the transfer switch work great in transferring power from one source to the other. BUT, I had it go wrong one time and the result was a fried converter (not a Monaco) and damage to my A/C control board.
With most generators you are transferring (from or to) both legs of 120v in-phase to two 120v out-of-phase sources (i.e. 220/240). The neutral has to cleanly switch (and if it doesn't then you might have 240v momentarily on your 120v lines) and both legs have to cleanly switch. Relays can arc, particularly under heavy load (which was the case in my situation). I also expect the quality of the transfer switch plays a role. If you remove all loads and perform the live switch-over, you'll have less risk of an Arc/surge, but they why not just shutdown the power and then power-up the new source. If your inverter is working, then the loss of power for a minute or two shouldn't matter anyway.
From my experience, I will no longer transfer power live, I'll switch off the power and restart the power so that the transfer switch is unloaded when it switches. I'm sure that many will, correctly, tell you that they have never had a problem. For me it only took one bad transfer for me to reconsider a live power transfer as it isn't worth the potential damage.