There is no paste immediately upon pattern switch.
But, you can paste over another pattern; while, the sequencer is still running.
So, a work around for live jamming is fill up some empty patterns with something simple, like, 1 bar, kick on the 1, and maybe a couple triggers on a track you usually have hats.
You have the pattern your jamming out on, save the kit, if you want to return to the pattern as is. Copy the pattern. Switch to classic mode so that the current kit is loaded upon switching patterns. Switch to one of the dummy patterns. Paste. Extended mode. Save the kit to a new slot.