To the second question: would I vote for a pagan?
[I doubt if one will rise to candidacy for president, but as for other offices:'
Would I vote for a pagan? I probably already have.
They come in many informal forms.

To the first question, about chaplaincy:
Some years ago I spoke to the chaplains' committee on endorsement, or whatever it is called: they check the credentials of the religious groups that want to be represented in chaplaincy. I've studied American religion for decades, but those two days I heard testimony from any number of groups that want to be in on the act.
Curiously, while Catholics, Jews, mainline Protestants are not producing enough chaplains--in part because their religious bodies have more dissesnters against recent wars, the less familiar, small, and, to others, "exotic" groups were ready to go. In some senses, it seemed that they welcomed this credentialing.
So it may be with Pagans.
since Chaplains are supposed to serve people of many faiths, and most do, it may be hard to picture many non-pagans welcoming services by pagan priests.
Still, on church-state grounds it's hard to know on what principle to rule them out: one does not want the government being the determiner of what is a legitimate religion and what isn't.
Some folks on both sides of this issue will get emotional about it, and most of the rest of the military and civilian citizenry will go about its business the same way, whether or not . . . .