@Woodchipper
For a long time, I had never bothered wondering how much thickness a coat of thin CA adds to a pen barrel's diameter.
Recently, I have been wondering so I made some rough measurements/estimates.
For a Sierra size blank, one coat of CA requires 4 drops of CA and adds (very approximately) 1/2 a thou to the blank diameter.
That info might be useful to you for estimating the answer to your question, which will depend on your method of CA application.
There are so many factors involved in each pen-maker's method of CA application that you pretty well have to do the measurement yourself.
My method of application is to drip the CA right out of the bottle onto the top surface of the rotating pen barrel.
At the same time as the drips fall, I hold a 1" x 3" piece of clear plastic up to the bottom surface of the barrel, rubbing slowly back and forth
as the drips fall. . The clear plastic is from a bag that pen kits come in, or I sometimes us bubble wrap for the plastic.
By rotating very slowly, I mean about 20 RPM or less. . I use the lathe to rotate and protect the lathe bed with a folded up rag ( 4 thicknesses).
Keep the rotational speed very low because you don't want to fling CA everywhere. . Electronically variable speed is essential.
After 4 such applications, I measure the diameter of the pen barrel. . I usually do about 12 - 16 such applications, then sand and polish.
So, usually this adds about 6 to 8 thou to the pen barrel's diameter. . It does vary, and the measurements are not terribly accurate.
By the time you have smoothed the surface of the CA the actual thickness is cut in half, roughly . . . . as I do things.