consecutive blackjack payouts

Has anyone studied the effect of a casino paying blackjacks consecutively, as compared to playing out all hands in order? For example, would a casino that paid blackjacks in the first and fifth seats, put both hands into the discard tray, and then played out the remaining hands, have greater "clumping", and therefore a higher advantage, given the tendency of consecutive cards to remain in close proximity to each other, even with a completely random shuffle? Should
casino's that pay blackjacks consecutively be avoided?

But some dealers will separate them when two or more blackjacks are paid at the same time (two cards at top, two cards at the middle,...,into the discard tray)
Probably instructed by the casino
So the first round is usually the easiest to be tracked

Why is it after all these years the only casino skill you've acquired is cardcounting?

"Consecutive blackjack payouts [are] good for shuffle tracking."

I have stood on soft 2-card hands when 2 or more naturals were dealt in the same round, to help the sloppy dealer do her sloppy shuffle without too much noise. The only condition is that the minimum bet is out.

For example, would a casino that paid blackjacks in the first and fifth seats, put both hands into the discard tray, and then played out the remaining hands, have greater "clumping", and therefore a higher advantage, given the tendency of consecutive cards to remain in close proximity to each other, even with a completely random shuffle

I have not seen any such study. You say "even with a completely random shuffle". I think this is a typo-with a non-random shuffle it does not matter at all how the cards are picked up.
I suspect any effects may be small, but it would not be without intellectual interest.