Not necessarily. If she loses, that loss can have that much more impact since we know what she's fighting for. ChouChou's backstory comes to mind as something done similarly. Nami's flashback too was told right before her money was stolen.
My two cents is Rebecca's role can expand beyond the confines of the tournament. If anything, since the Revolt/attack on the factory is about to happen, her time in the tournament could be limiting her since at this point it looks like the raid on the factory will be happening around the time the 4 winners face the Doflamingo family.
Given Doflamingo's line to Law and the Vice Admiral's query about why no participants have left, presumably something sketchy is happening to the losers. I'm not saying Rebecca should be a damsel in distress, but at least she'd possibly be closer to the action and the Toy Soldier that way.
And well, the fight for the Devil Fruit seems to be a spectacle unrelated to the rest of the arc. Bartolemeo and Burguess definitely have nothing to do with the arc's happenings. Just think keeping Rebecca there as well doesn't have to be the only role she will play in the arc, though her going all Gladiator could be intriguing
Normally, I would probably agree with you, but both Nami and Chou-Chou's flashbacks led to situations that had near immediate solutions. Nami's flashback leads to her money getting stolen which leads directly the march on Arlong Park, a classically strong moment that resonates in the minds of most readers. Similarly, Chou-Chou's flashback has a near immediate response when Luffy bests Mohji and Richie. If there was some sort of easily resolvable situation or action that Luffy could take, I might agree with you, but even if Rebecca loses to Cavendish, he's not really part of the internal workings of Dressrosa. Luffy beating up Cavendish doesn't really solve Rebecca's problem or resolve any of her plotline, so this really doesn't strike me as a flashback where we're specifically learning about someone's motivation and resolve to make their defeat that much more resounding. Plus, considering the way Oda's written this arc, we'll very likely be switching focus over to the Green Bit side and/or the Tontattas and/or the Thousand Sunny crew before D-Block is fully resolved. I think that if Oda specifically wanted to expand upon Rebecca's motivation prior to her defeat, he would've skipped the flashback, left in the part regarding her getting booed and the prisoner gladiators explaining to Luffy why that's happening, and then revealed her motivation in the middle of the bout, right before a climatic moment.