Yes for verbs ending with poner, but compone/compuso is not the tu' form of the verb. It goes with Ud./el/ella.
I can't say for certain if the same rule applied to all irregular verbs with identical endings.
SraJMcGin may post an answer to that later.
Yes, the verb componer follows the pattern for poner, exactly, just with the prefix "com" there.
poner = pongo, pones, pone, ponemos, ponéis, ponen
compouer = compongo, compones, compone, componemos, componéis, componen
poner = puse, pusiste, puso, pusimos, pusisteis, pusieron
componer = compuse, compusiste, compuso, compusimos, compusisteis, compusieron