Don't you think with the current drastic spikes in demand it's not really possible for any service to keep up? In regards to human ressources you always have a very slow adaption to the demand. You have to find qualified people and train them. You can't really just buy some more capabilities on demand, like with servers, at least if you want to keep up QoS.
That's why I'm saying it would make sense to make an announcement, add a notification to the dashboard after log in. It's really simple and does not require to hire more people. However, it does require you to implement more customer-centric thinking and work smart, not hard.
Example? There is an automated message when you submit a support request. All they had to do was to add a precise information "due to extremely high traffic we are experiencing unusual delays. We will do our best to get back to you within 3 business days".
That's it! If I would have received such message, I'd sit back and relax until Thursday.
There are many circumstances you may use as an excuse in every difficult situation. The point is not to look for an excuse for not doing something. The point is to find a way to do it despite circumstances.
Ok, then I got your post wrong. That's totally fine by me. Such a notice/announcement would be the best way to cope with the overwhelming workload and would be for sure the most user-friendly way. The worst you can do is letting your customers in uncertainty about their current situation.