Children wouldn't work for oh so many reasons. But what they could do, is have some kind of a time-warp thing like in the Mysts o'Time on Lucre Island in MI4, except a warp that lasted the entire series. Here you could have an older Guybrush and Elaine (I believe TT actually did this briefly for S&M?) and also Guybrush's kid, whose only slightly younger than Guybrush: awkward!
That would be a vaguely interesting concept, and one that could be "undone" by the end of a season.
I agree with your view on their dynamics as parents, though. I can't see Guybrush being responsible, but also I reckon he'd definitely care for the little kid.
Ooh how about this one... They don't know it, but Morgan La Flay is Guybrush's daughter from an affair with... Winslow?!

Well Arnold Schwarzeneggar managed tohave a baby in that film thing...