Using the B would mean saving time and money on not having to built a new model for the Ambassador class. That's the only real way the episode would have been different.
Yeah, this is the most likely scenario:
Writer: “I just wrote this great script where the Enterprise-C gets thrown forward in time 20 years and meets the Enterprise-D, but history is changed and they’re at war with the Klingons. Denise Crosby is even coming back.”
Producer: “That sounds awesome! Let’s do it!”
Writer: “However, we’ll need a new filming model built for the Enterprise-C.”
Producer: “What?! We can’t afford that!”
Writer: “ Well, we can’t really do the episode without a ship for the Enterprise-C.”
Producer: “We have all those movie models lying around. Use one of those. Add some fins or shit onto it to make it look different.”
Writer: "Uh, ok. Well, we're also going to need some new Klingon ships."
Producer: “What?! We can’t afford that! Just use that bird of prey ship we always use."
Writer: "But we need large battlecruisers that are a match for the Enterprises! The bird of prey is a small ship."
Producer: "Then pretend that that little bird of prey is a big huge ship. Have the vfx guys do some trick camera work or some shit."
Writer: “Okay, well we’ll also need some new uniforms made for the Enterprise-C crew, and some new phasers and commbadges.”
Producer: “What?! We can’t afford that! Use some old movie uniforms. Find a gun out of the stock prop bin. Find a movie pin and use that for a commbadge. But only give it to the captain because we only have one.”