Maybe. If they can sneak in attempts of Metal copying data from the crew. Or if they have their own twist on that, I'd be interested. So long as Metal reaches a breaking point to be "the one, true Sonic", the cravings of power to outdo him could grow and lead to Overlord in some form or fashion.

"...the robotic villain remains loyal to his creator post-death, which would fall in line with the character's motivation in the video games." Not even remotely. Metal HATES Eggman. It's betrayed and is always willing to betray Eggman on so many occasions to get its way I wonder why he keeps attempting to rebuild it. Metal acting independently is not only nothing new, that's its main personality. To use whatever means necessary even if it has high costs for one purpose; prove it's better than its organic counterpart. So even if Carrey doesn't come back, we can easily assume with Eggman out of the picture, anything shackling Metal back is broken. The only thing that needs to develop is its rivalry to Sonic.