Will a yeast two-hybrid assay work using an integral membrane protein as the 'bait'?

Definitely do not use the transmembrane part. It will give you lots of problems and also think of it this way... if it gets integrated in the membrane what are the chances that the complex with the "bait" will be able to reach the promoter of the genes for auxotrophy and activate their transcription? Probably zero. If it doesn't integrate it could aggregate because of the hydrophobic stretches.

The problem is the 3D-structure. When you don't have all of the protein you could have a different conformation which doesn't allow binding or promote binding of other proteins which are not normal partners of your target.

Anyway two-hybrid is more of an indicative method and you can't prove only with it the interaction. You should clone both combinations (the viral protein domain in either vector) because slight orientation matters and linkers are important. I had two interacting proteins Y and A and cloned in the two vectors (a and b). In theory both combinations aY-bA and bY-aA should have worked but only bY-aA did.

I don't know exactly your experiment but you could do a literature search on the TAP method developed by Bernard Seraphin at EMBL something like 1998-2001 for identifying interacting partners.

It also depends on the oligomeric state of the protein and number of transmembrane passes. Dimer receptor molecules have been approximated quite successfully for E.coli chemotaxis by substituting the TM with a leucine zipper. I think, but could be wrong, that something similar has been done for the osmosensor of E.coli EnvZ. You should look both up if they suit your case.

The standard yeast two hybrid screen (YTH) tends to not be effective in determining interacting partners for membrane proteins. While you can use a domain of the protein without the transmembrane region(s), you risk losing the seconday/teritary structure responsible for the protein-protein interaction. Additionally, since the interaction in the traditional YTH takes place in the nucleus, cytosolic co-factors that may be involved in interactions may not be present in the nucleus. Both of these problems can be avoided using the modified split-ubiquitin YTH screen. The one disadvantage on this approach is that you have to generate an new screening library, which can be expensive in time and money, however there are companies that will generate a library or you.

The TAP system is a good suggestion, and it does avoid some of the troubles with the secondary strucuture and cytosolic interaction, but if you have more experience with yeast it might be easier to stick with the YTH. Also, for the TAP system you have to do a lot of mass spec (MALDI) to determine protein srequence, while with the YTH you get nucleotide sequence. If you have easy access to MALDI, you might be better off with TAP.