I'll expand your question a little bit to ask, "what recourse might the MWC have because of this poaching?" Regarding a claim against the Pac-12, the first answer that comes to mind is not breach of contract, because the MWC and Pac-12 aren't in any type of agreement where a prohibition on poaching a team makes sense (unless they built that into their agreement to play football this year). But, tortious interference with a contract might apply. Essentially a party like the MWC in this scenario would have a claim against the Pac-12 because the Pac-12 interfered with MWC's agreement with Boise St., for example. There would be loads of questions about how damages can be calculated, but that's for actual lawyers and accountants on the case to decide.
Another recourse for the MWC might be breach of contract against Boise St. But I have a very good feeling that in lieu of making a claim like that available to the MWC if Boise St. leaves, the MWC requires the substantial buy-out amount.
Last couple notes on the tortious interference claim: MWC would never go after the Pac for that because it would open the flood gates to every other conference suing another conference each time a school moves. The MWC wouldn't want to sue the Pac to get some sort of damages for Boise St. leaving, and then turn around only to see C-USA to get the bright idea that it can sue the MWC for poaching TCU from many years ago (that's the latest example I could think of). Also, very likely that the NCAA, which charters the conferences and governs their administration quite a bit, has prohibitions on retaliatory litigation in the case of a school leaving.
tl;dr: No, MWC probably wouldn't have any claims for many reasons.