The real test would be if you had a franchise as willing to pay high in a low tax state that had a good shot at winning, would players prefer it? You'd think Houston might be that sort of franchise, but the management seems to be hard for some players to take. In the NBA, did the tax situation help the Rockets / Spurs / Heat v. the Knicks? who knows how much of a factor it is.
If it is $800K on $10MM AAV, it may be a factor forcing the Yanks to offer $11MM if they believed they were bidding against Houston, but probably not against the Rangers. I'll guess the Rays mention this as part of why their lower offers are worth more than what other teams offer unless they are beat substantially.
VA is probably a low tax state relative to PA, MA, NY, and CA. It probably is a plus for the Nats.