New XP Upgrade Disc & Old 98SE Disc

I have an old desktop that I have loaded a xp upgrade version onto new or cleaned hard drives over the years: start with the xp disc. that will run a short time,will ask for the 98 disk for a moment (its product key is not requested), then finish the rest of the 20-30 minute installation with the xp & activated with its key. This old pc still has some uses.

I now want to load xp onto a newer desktop ( mobile racks used to switch operating systems,here) with another (new) xp upgrade disc but have this question: will this installation still work using the above "98" disk & not run afoul in the final activation of xp?

Thank you