Yeah, I mean, it depends on the context and who you’re pushing back to (your boss vs. other coworkers, etc.), but in general, I agree with garli here. It’s a good idea to be upfront whenever your workload is starting to get out of control. If the humor is being used to soften the message, it might be getting in the way of that.
While vague warnings might help in certain contexts (like communications to peers), managers are going to want more info: Why are things falling through the cracks — and what things are falling? If you haven’t started studying something yet, what have you been doing instead?
Being clear and matter-of-fact will avoid follow-ups and unnecessary managerial concern. Saying something like “I’m behind on X because Y took up so much time, but I’ll get to it by the end of the week” demonstrates that you’re on top of your priorities — and that you have a handle on your limitations.