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Imho.
Time for empirical testing!
The DUP would not, in this hypothetical situation, matter if Labour voted for the referendum in the hope of then leveraging a no-deal result into a GE. That's a bit torturous as a chain of events though, I would think that they'd vote down a referendum to bring down Mays government and get the GE. However, they're trailing the Cons by 4 points in the latest poll (I know, right!), which means we might get another Tory gubmint.
Imho.