I've seen variations on that. You still need to work out what to do with the quill to match, make a new one and lap it to the bore would be one solution. Moglice is another? The preferred solution from classic machine rebuilders seems to be to have the tailstock cylindrical ground, then the quill chromed and ground.
With the method shown, I'd want to bore the collar in the chuck in-place in the chuck without removing it before doing the tailstock, to eliminate any runout from the 3-jaw chuck, or dial it in using a 4-jaw. He does mention in the comments using a boring bar in the chuck to bore the carriage support.
I'm going to need to do something with the tailstock on my CK but haven't come to any conclusions on how I'll proceed.