Personally, I received a TC offer with a month-long deadline, while waiting on another outcome. In the last week of the offer, I reached out asking to extend the deadline, which the firm refused. So on the final day, I just accepted and signed the offer. Heard back shortly after that I did not receive the second offer anyway. Everything has been fine, though; no negatives to accepting on the deadline.
I would also say there is no negative to reaching out. As applicants, we overthink every communication, but provided your email is polite and to the point, grad rec will literally glance over it, reply, and not give it a second thought. Certainly, I've been explicitly told before by firms that the decision process can be expedited if we have competing offers, and to let them know.
