I don't know for sure actually. definitely Sauron would have commanded the Balrogs during the Years of the Trees when Morgoth was imprisoned by the Valar. but then the Balrogs fled and scattered during the War of Wrath when Morgoth was defeated at the end of the first age. and then my knowledge of the 2nd and 3rd age history is pretty fuzzy, so I don't know if Durin's Bane (or any other Balrogs) would have been in contact with Sauron, or if he tried to regather them (which I imagine he would if he knew of any that still existed), or if they were all just isolated in hiding for thousands of years. but in any case, if the confrontation with the Fellowship had gone differently, Durin's Bane might have been flushed out of hiding, and gone out into the world to discover that Sauron was regathering his forces, and in that case I don't see any reason why he wouldn't agree to ally with Sauron