Generally speaking, no I don't see Lois supporting Clark in such an effort.
However, it depends on how Clark is trying to achieve his goal. Is he literally taking over the world as a benevolent dictator, or is he doing something a little less obviously evil and flawed? Every story we're talking about here has gone the "tyrant" route, from Justice Lords to Red Son to Dominus to Injustice, and in all of those Lois has rightfully left him (if she's not already dead).
But Clark representing earth in the United Planets (a position he sort of fell into) presumably comes with some political power and clout (we've seen him commit earth to at least a few policy decisions), and Lois is perfectly fine with that.
So "Supreme Leader Superman" isn't anything Lois would get behind, but "duly elected President Superman" might be another story. But that's a tale I don't think we've ever really seen, outside of a couple old Silver Age "What If?" issues.