Could the no-hole-card way of dealing a game, where splits and doubles are not lost, change strategy against a 10 or ace when playing such a game?

My first thought is 'no', but being I am not good at mentally fathoming the Monty Hall problem, nor understanding why the push-22 rule changes strategy for BJ Switch (had to prove it to myself empirically with a sim) I'm open to the possibility that being you won't lose your extra bets when the dealer rolls a natural, the house edge on that extra bet becomes zero instead of 100% in case of a natural, and that dilutes the remaining probabilities to the point where the strategy changes.

The particular game I had in mind was Multiple Action, which is essentially a NHC game repeated 3 times.