If Catelyn were pregnant in GoT and gave birth to a healthy baby boy, would the plot change at all?

Well, yes. The pregnancy and birth would certainly prevent Catelyn from being as mobile as she is. Likewise, having a son of the House of Stark alive in the South would definitely change the plot – the “deaths” of Bran and Rickon wouldn’t be as consequential in terms of feudal politics, it would probably change the second siege of Riverrun significantly, etc.