In short no, but there is a way of doing it that will require some manual input.
Once you are down to 14 players you can insert a further 3 seats at your last table, and check the box on Tables Tab > Settings > Automatically Randomize Seating at Final Table
You can also check the box at the bottom of the player movement dialogue "Display Player Movement Screen when Movement is accepted"
Now for the event, all we can do for the event (I believe) for what you are wanting is to have it fire when the 11th ranked player busts is to pause the clock, so create an event;
Events Tab > New Event > Predefined > Player Busts Out > Conditions: rank = 11, Actions: Pause the Clock.
So what that does is when you bust the player ranked 11th:
Pause the clock,
suggest player movement for your 10 handed final table (provided you have already set up 10 seats on your last table in use).
click ok move players
the player movement screen then displays, which if you don't use could be altered to suit the needs of the final table.
EDIT > Ive just notice there is a further option "Automatically accept player movement suggestions" in the Tables Tab > Settings, but the only problem is that's grand for your final table but depending on how you run your games probably not so handy when your balancing and collapsing during the game.
Hope this helps
Stu