Drexel has an NAAB-accredited BArch program, so a graduate would not need an MArch degree afterward.
However, agree that the $104,000 debt is a bad idea, if it is even possible (cosigner or parent loan required). Especially since pay levels are not that high. (It is not really a STEM field, and STEM does not necessarily mean high pay anyway – just as a biology major who did not get into medical school.)