Could rose cuttings (after being rooted) be braided to create a thick base stem? I've seen it done with many plants but never roses.

Try it and let us know how it works!

Not sure how that would work with a thorned rose but maybe one of the thorneless ones! Reine des Violettes?

But do remember that, if the rose is rooted, it will soon put up thicker, more mature canes all on its own.

... and unless you remove the bud eyes, it will send out numerous shoots along the stem. Try it!