I don't see why a breakup would mean a Firefox deal can't be done anymore. Unless the search engine business shut down, they would still be motivated to have a default search engine deal with browsers.

What might change, I think, could be:

• Search engine may be way less motivated to have a deal with Firefox. FF has pretty low market share. One popular theory is that Google continues to subsidize FF partly to make it look like there is other viable browser competition and that they are helping foster it (for antitrust reasons). If search and browser were different companies - not being proposed I don't believe, but could happen in a breakup - this might lessen. Although apparently even 2-5% of the market is worth billions so I could see it easily continuing. Especially if signs are that other browsers start losing some share.
• Less money to FF: If the ads biz does become less lucrative, that'd flow downstream to deals like the one with Mozilla.

But I don't see any reason why they "wouldn't be able" to have a deal anymore.