Barring going to work for a multi-national as a full salary foreign employee with benefits no one will care what you did in China. Working as an English teacher gets you nothing back home in the West.
....unless you come back and look for work as a teacher . . . just sayin'.
It's something I find to be an extremely likely possibility for myself. Having essentially sacrificed any professional career I might have had on the altar of CMA training, my sister, a school teacher herself in Los Angles, is always recommending I go that route. I have a degree in Chinese and Chinese is being taught more and more in the states, especially at high end private schools.
Having done both, student and teacher in China, if you can afford it, I definitely recommend the student path. Teaching ESL can be as difficult as learning Chinese. Depending on where you work it can be quite challenging to do properly. Some people take right too it. I think teaching adults is a hell of a lot easier than a room full of rowdy kids.
Having a place to stay will happen regardless of going the teacher of the student route. Most ESL jobs offer accommodations anyways. Just make sure you make arrangements before you go because, yes, the Visa regulations are
completely different from a few years ago. This year was a rude awakening for me as I arrived on a tourist visa, as usual, and neither my employers (a major University with close government ties) nor my friends in the Public Security Bureau were able to help me avoid leaving the country and coming back in again.
If you don't enroll in a school (and it doesn't have to be a University with transferable credits unless you are doing this as part of a degree program) you will very likely not learn much Chinese, especially in Beijing. I've not met anyone ever with Chinese worth a damn who did not at least have a very solid foundation in a formal learning environment. The immersion accelerates things and you learn to hear and understand but you will just not learn to speak it without instruction. The people who have lived here for years and can barely speak Mandarin that Peacedog mentioned are not the exception, they are the rule. (sad to say) There's enough English speakers and ex-pats around in Beijing that you really can live without it,
especially on a college campus where the entire student body is cramming to pass their "Band 4" or "Band 6" English exams to graduate.
Anyways, having a job or a school helps A LOT because you have not just a place to stay but a structured life, instant peers/friends, people to turn to for help with whatever you need help with and so on. If you are going alone and don't speak Chinese, your employer or your school can be a great ally. Free yourself of them ASAP ...but when you first arrive, it's good to know they are there.