if you connect up to the controller (like you would earbuds) then yes, its not a hard setup to use equipment your'e talking about.
the xbox branded adapter is likely overpriced. it should be a standard 4pole 3.5mm headset jack. you will need an adapter yes (to split from the 4pole 3.5mm to two separate 3pole 3.5mm jacks for mic and headphone). these are often called headset adapter cables, pc headset to console adapters or various other names and are often fairly cheap (can be $2-5 at cheapest for low quality ones)
controller->splitter->amp->headphones. if you use a microphone (such as modmic) you will go direct to the mic side of the splitter (no amplifier).
check out amplifiers from fiio. the a3, e09k, e11, e10k, e17, e12 would...