It is going to be concentric as you are turning it in place on the spindle. If you are cutting in the bore, same thing. Just like turning a part deep in the chuck. I can't say though that I would risk turning an already thinned spindle bore in place on the lathe. How much has it been thinned? How much more can you take off before you have to worry about it deflecting under a heavy cutting load?
It doesn't have to go down in the bore of the spindle. It would be a pain to put in and take out anyway. Just make a collet holder that fits on the end of the spindle like a chuck. You get the advantage of the larger bore and don't lose that much room on the bed. A 5C collet holder is about the same thickness as a chuck. An ER holder is much thinner. Personally, I prefer the ER collets for their wider gripping range and easy accessibility. I have an ER32 on my lathe and mill, and a spindle collet chuck for my wood lathe and only have one set of collets.
It doesn't have to go down in the bore of the spindle. It would be a pain to put in and take out anyway. Just make a collet holder that fits on the end of the spindle like a chuck. You get the advantage of the larger bore and don't lose that much room on the bed. A 5C collet holder is about the same thickness as a chuck. An ER holder is much thinner. Personally, I prefer the ER collets for their wider gripping range and easy accessibility. I have an ER32 on my lathe and mill, and a spindle collet chuck for my wood lathe and only have one set of collets.