I don't think so. It sounds like the tax will be set by the Feds, and they'll simply pass on the responsibility to police companies and to collect the tax to the States, likely in exchange for a %, maybe even most of it. So it will be neutral in terms of jurisdictional competition.
Discussion
Oh... Makes sense. Too good to be true.
It's just my speculation though, based on the fact that this would be a federal tax. It could also be something like the Feds setting a bracket with a minimum and a maximum. In that case yes, there would be some room for competition, albeit mitigated.