According to PMEG: "Post movaj verboj kiel iri kaj kuri, oni preferas I-verbon sen rolmontrilo, sed ankaŭ eblas uzi por." So, yes iri x-i is correct and means the same thing as iri por x-i.
Note that, as vangelion said, these phrases involve actual movement/going, so some English phrases such as "go to sleep" which don't necessarily involve a change in location, may be better translated in other ways (e.g. "to go to sleep" -> ekdormi, enlitiĝi, etc.).
EDIT: based on the comments I should clarify, sometimes "go to sleep" does involve movement to a different location, in which case iri (por) dormi or iri kaj dormi would work, but when movement is not involved (e.g. "You shouldn't be reading in bed. Go to sleep."), ekdormi or endormiĝi would be better.