I'm curious, I have never tried upgrading a armor with accessories on it
If I upgrade my armor, do the accessories on my armor stay on it as I upgrade?
yes they do
Mostly yes. But they don't stay on the armor if they are unable to, because the upgraded armor doesn't have that slot. (Admittedly I don't know of specific examples, because I don't care about accessories.)
This is a classic example where a really good answer is already available in multiple places on the wiki. The answers that you get in a forum thread will be no better.
The Grey Feather Cowl
Say you have a Glasses accessory on your Miracle hood (magic hood 4*) because it has a front accessory slot, if you were then Upgrade you Miracle Hood to a Grey feather Cowl then the Glasses will be destroyed because the front accessory on the Grey Feather Cowl is not doable but in this case it has a 'built in' (?) prismatic eye glow
same thing applies to armor
if in the same scenario you have glasses and a miracle hood and upgrade it to a chaos cowl since the front accessory has nothing and its doable then it will be transfer from the miracle hood to the chaos cowl
*again same thing applies to armor
Try reading the wiki page "Accessory". Or try reading the "Upgrading" section of the wiki page "Crafting". I hope this helps.