Does securing a supervisor basically guarantee acceptance? I received an email from a prospective supervisor telling me he'd like me to join his lab and that he'll forward my name to the grad office. Assuming my entire application is strong, does this mean an official acceptance is very likely? Or is there a chance I could still get rejected by the admissions committee? This is for a funded PhD program.
It depends on where the funding comes from. If the money comes from the professor's own grants, then you're extremely likely to get a formal admission. If the money comes from the department the professor now has to convince the admissions committee that you should get the position. Why not send an email to the potential supervisor and ask what the next step is? That should let you know where you stand.