One of the biggest reasons why BS is different for 1 deck than it is for 6 decks is because; in a six deck game,the effect of removal of each individual card is less important than single deck. For this reason; if you're counting cards then there is a TINY bit of truth to your hypothesis. But if you're counting cards, you won't be playing BS anyway; you'll be using your play indexes.
Example: Off the top of a six deck shoe (TC and RC is 0)you're dealt a pair of fives, dealer has a 10 upcard. You hit & get a six. BS and your count strategy tells you to hit again.
Now let's suppose five decks have been played, and the count is 0. If you're NOW dealt this hand, these 3 small cards in your hand have NOW changed the TC enough to enable someone who's counting cards, to stand.
But like I said, there is really only a tiny bit of truth to this. The GENERAL answer to your question is: No - BASIC strategy shouldn't change.