Can "should" be used to mean "if" and used to mean "would" in the same sentence?

It's perfectly possible to use two shoulds in the same conditional:

Should anyone phone asking when the drilling's going to stop, I should imagine we'll all be finished by 2 o'clock.

Of course, it's not strictly accurate to think that the first should here is replacing if. Here's the same sentence with if reinserted:

If anyone should phone asking when the drilling's going to stop, I should imagine we'll all be finished by 2 o'clock.

Here we can see both if and should together in the same protasis. The first sentence uses subject-auxiliary inversion to mark the conditional protasis. The if has been dropped and the Subject, anyone and the auxiliary verb should have changed places.