Using a custom spawn egg on a monster spawner will change the spawner's mob into that mob, but it will not have any of the custom tags. There is an exception for the Husk, Stray, Cat, Elder Guardian, Wither Skeleton, Donkey, Mule, Skeleton Horse, and Zombie Horse spawn eggs. However, giving yourself a custom spawn egg that spawns these mobs will also not work on spawners.
P.S. Sorry the pics are in a weird order I didn't want to redo them all just because of one mess-up