If extra (not required) recommenders don't submit recommendations by the deadline ...

… is it a problem? Will the college consider the application incomplete?

For example, one college only requires a counselor recommendation and one teacher recommendation, but allows more. We assigned a couple of other teachers, but only the counselor and one teacher have submitted a recommendation so far. If the EA deadline passes and the others haven’t submitted anything, will the college still consider it a complete application?

Even if the required recommenders do not submit on time, it’s not an issue for almost all colleges. The applicant needs to get his/her piece in on time, but everything else generally gets a slight grace period.