Honestly? No. It's one of those things I grew up hearing, which seemed to make sense. Doing a quick search turns up papers like "Do exit polls influence voting behaviors?" which are locked behind pay walls, but the excerpts seemed to indicate that there is an effect scene, albeit a small one, on West Coast voting based upon East Coast exit poll results.

As someone who has studied political science, presumably you may have better access to those scholarly articles than I do.

Anecdotally living on the west coast I know folks that didn't go out to vote because of early projections from the east coast. It was more common in the past where you might have to wait in line for an hour or two in lousy weather, but most folks I know now do early voting.

My understanding is that they have limited impact because most of the western states are not competitive at least in presidential elections.

And in midterms the effects are localized anyway