Is wood glue a can-do with dyed woods?

I’m going to build a jewelry box and use dye to add color. I’d like to dye all the small parts, such as the tray dividers, before assembly to make it easier. Will glue adhere to dyed wood?

ELMER'S Carpenter's wood glue Off-white, Quick Dry Interior Wood Adhesive (Actual Net Contents: 4-fl oz) in the Wood Adhesive department at

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