HI,

I think classes for colleges will continue to work in online mode so as such there will be no issue. But suppose if yo complete both your diploma as well as your BSc and then wish to apply for a job then you can't mention that you did both the courses as a regular student that too in the same time period.

There are many students who prsue two degrees at the same time, but they just ignore that sometimes while taking admission  the university takes your approval that you are only enrolled here on a regular basis and not in any other university or college. If they found out they might terminate your course so you need to be careful.