Can I use 在 with 一边... 一边?
[一边 (verb A) 一边 (verb B)] indicates  (verb A) and (verb B) are carried out  concurrently. Please read Is the 边～边 the synonym for 一边～一边? for reference
[在 (verb A)] indicates (verb A) is in a progressive tense (in the middle of doing it / in a continuous state of doing it)
Neither structure indicate tense, because Chinese verbs do not inflect between present and past tense. Please read How do you specify past tense for 是? for reference



  我一边在吃饭，一边在做作业


It is not technically wrong, but the more efficient structure to express the same meaning is "我在边吃饭，边做作业" 

[边] 吃饭 [边] 做作业 indicates "eat dinner" (verb A) and "do homework" (verb B) are carried out concurrently

[在] [边吃饭，边做作业] indicates both actions are in a progressive tense (in the middle of doing it / in a continuous state of doing it)