Yep, it would work.
I tested this with a replay also, and, as we can see, the Entei used Burn Up, burning itself out, and then it was immune to all the moves done by the Barraskewda, even an otherwise super effective Liquidation, and Max Geyser.
But, even though it'd work, it's a very trash thing to play with in Pure Hackmons, where things like Photon Geyser (if Gen 7 and up) and omnipresent. In Gen 6 PH, which is, by far, the most popular Pure Hackmons metagame, this strategy would still suck, as Mold Breaker, Teravolt and Turboblaze is almost on each and every team, as they can hit Wonder Guard this and that also.
Hope it helped!