It's would be really hard to provide any number. It will be different for different devices and possibly also different versions of iOS and what else is already running. Unfortunately trial and error is what remains.

Would it be possible to provide the user with an error message instead of letting the app unceremoniously crash?

We did spend a fair amount of hours trying to do exactly this, but it's very hard for the app to predict the total amount of memory required in advance and once we have used too much the OS is very brusque. We will likely be revisiting this topic with some regularity in hope for a solution.