It makes sense, as folk etymologies often do. But the phrase acts in a more conditional manner in Southern American English at least.

If I say "I'm going to change that light bulb," I'm probably already getting up to fetch my toolbag.

If I say "I'll try and change that light bulb," I may be wondering whether I have a spare or a ladder or something else whose lack will interrupt the job, or in some other way doubtful of success: the implication is I expect I may come back and say something about the job other than that it's done.

If I say "Well, I might could try and change that light bulb," I probably don't mean in any particular hurry even to get up off the couch, and indeed may already be dozing off.