Not a smart move to intentionally pay twice..
Not really paying twice so much as "loaning" (yes at 0%) the money somewhere. The questions are, who is holding the money, for how long, what's the value of using a credit card on this transaction and tallying up if it's worth being out that amount for that time for the reward (SUB?/Other?).
Unless you're dealing with a sketchy institution that'll make your money disappear.