Hi Mike,
There are a variety of points within a given system in which delay can be introduced.
In your case, yes, genlocking certainly may help. Indeed, as the HS410 manual details, there are points within the switcher itself in which path delays can be accrued – inclusive of using PIP. Depending upon other aspects of your configuration, there may be other points of delay. However, it’s hard to say more without knowing more specific detail about the show, and both your post and production needs.
Needless to say, while there will always be delays in a live system, the name of the game is managing and minimizing them to make both production and post easier.
-Denis
(been there, consults on that)