That could very well be what happens, but then where's the depth that every team needs when injury hits? all they have left are minor leaguers with 0 big league experience at that point. Sure there will some last minute minor league signings with invite's to spring training, but I don't think that's what they team should be shooting for.
If anything, they should be looking to add at least 1 big league arm, with Pearson starting the year at AAA (along with Logue and Francis), in his last option year to get stretched out, and he be the first man up when injury hits, assuming his health and command are good. Kay and Hatch are probably also 5th man rotation options but to me it would be better if they were the depth, not the 1st option.
I think Hatch still has options, but Kay might be out as he's been up and down for 3 seasons. Kay might have the inside track on #5 as it stands right now and that's probably not ideal.