Whether you can stay on campus with a GED depends entirely on the specific college or university's policies. Some institutions will treat GED recipients the same as high school diploma recipients, allowing on-campus housing. Others may have restrictions or different criteria for on-campus housing eligibility that are not solely based on GED vs. high school diploma.
To find out if you can live on campus with a GED, you must contact the housing office of the specific college or university you're interested in attending. Their website might have information on admission requirements, including housing, but it's best to confirm directly with them.