I don't think SSBI will get cleared if there are some issues in his immigration status.Probably they used to ignore it before but I dont think they do it anymore. coz when I was having my SSBI, the investigator asked me to give him the copy of my spouse I20 to check her status.If any enlistee is married to illegals they wont let him ship out.
Yea sometimes army will let Mavni to ship out but they have to stay in reception until the investigation is completed.If someone get kicked out from reception coz of ssbi might happen but kicking out from BCT coz of asylum application is unlikely to happen.