My SEA antenna tuner automatically connects the antenna output to ground when if the off state (a good size relay disconnects them before tuning). I have seen massive antenna switches at the base of the antenna do the same. The question of course is how much would an antenna switch help?
If it is a backstay, properly grounded, you can hope that most of the
current goes through the
mast and a tiny portion goes to the backstay, hence the tuner disconnect will help. Yet, the
current will find its way throughout the
boat even through the ground connections and still fry everything.
I think the only way to be sure is to disconnect the tuner, radio and all
electronics completely and wrap them in
aluminum folio. I would not bother unless lightning strikes were a frequent event in my area.