It's not really that valuable (to you) to worry about "the site" being "overloaded". What's more important to you is how many people are watching the major tags of your question, pde in this case, and how busy that tag is. That is, what you'd really care about is whether the pde tag is "overloaded". What do you care if there are 1001 unanswered pre-calculus questions a day? I would assume (hope) that the people watching that tag (or any relatively "advanced" tag) are doing it so that they can filter to the questions they are interested in answering rather than trying to pick them out of a flood of uninteresting-to-them questions.
For pde, there are 366 watchers and 13,155 questions. The least recent question on the first page (at 50 a page by default) is from November 22nd, or five days ago. Compared to the tags I actively follow, logic and category-theory, the number of watchers seems low for the number of questions. I have no idea what an "adequate" amount would be, and it would obviously depend on the amount of effort typical questions required as well as the people watching that tag. At any rate, it seems like it would take a while for a question to get buried for the pde tag. In other words, it's unlikely that a "regular" of the pde tag will fail to see your question entirely.
The story is similar for "typical wait times". Certainly, a site-wide average would be useless. Even an average restricted to pde would be of questionable value (and I suspect it has a long tail). I've answered plenty of questions days or even weeks after I've seen them, let alone when they were asked. Sometimes it's because it takes that long to make a good answer. Either way, I feel no urgency in answering. My understanding of StackExchange is that the (nominal) emphasis is overwhelmingly on answers that are continuously useful to more than just the OP. While obviously unanswered questions are likely not that useful, rapidity of answering is not that optimized2.
Most of the highly upvoted unanswered questions (for the tags I follow) just seem genuinely hard to answer. From the comments, it sounds like your question is not in that category, so I suspect your question will eventually be answered, but I have little idea of when. If the answer to the question is important for you, you should be working on answering it yourself. If you do, you can self-answer the question. If you need a more timely answer and you're a student (though it seems like you aren't(?)), then I would suggest talking to a TA or tutor.
1 This is a made up number.
2 Though it is usually advantageous reputation-wise to be the first answerer assuming your answer is adequate.