Good question.Sounds like a good shout tbh if you have that option to be doing the build prior to moving in.
I'd 100% be doing that personally over trying to exist alongside a large building project at home. I detested every minute of it, especially towards the end when a random tradey would turn up in the morning to do a job and a random trades would then turn up in the afternoon to finish a different job...was so frustrating.
Is there a view on the value of the house post build completion and whether the build costs would add enough to the value to be in positive equity?
I'll ask the estate agent what they would value it at if it was done.