So, if I built up a 29″ rim (with a braking surface) would it fit on a road bike? Or would there be problems with the caliper brake not fitting properly?

The diameter is the same but the width will dictate calliper adjustment & tyre profile.
I use a 25mm inner width rim (Pacenti from Superstar) on my disc braked road/cx thing with 30mm tyre.

My first 29er had Mavic road rims, as 18Bikes could not get hold of MTb specific rims. This was in 2006iirc.

The latest trend in road rims (i.e. wide) are the same with as some of my old 29er wheels!

As long as the brakes can handle the extra girth there is no reason a 29er rim shouldn’t work are a road bike rim. Bit heavy duty maybe.

As long as the brakes can handle the extra girth there is no reason a 29er rim shouldn’t work are a road bike rim

Careful though as some MTB rims (especially Stans) have a max pressure that means road tyres may not be a great idea unless big low pressure ones.

I thought the max pressure on Stan’s rims was only applied if you are running them tubeless?

Plenty of people running roadie tubeless though, and even with tubes, depending on the tyres you choose to use I would be wary about very high pressures on small tyres on some of the wider Stans 29er rims.

In all likelyhood you’d be fine but I’ve seen enough blown slicks on MTBs over the years to at least be wary and put some thought into which combos to use.

How many 29er rims do Stans make, with a braking surface?

Clearance to frame and fork may also be an issue to consider, it’s a fairly extreme example, but we have bikes running 23mm tyres that 25mm tyres will cause rubbing on.