By all means ASK the printer, let them know of your concerns and have them satisfy you that this will be accounted for and will not be a problem… but don’t try to second guess them with your setup.
Again, assume nothing and ask the printer how they wish for the file to be supplied. Such as one complete file for a 52 page job or perhaps as a separate file for the 48 page text section and another separate file for the 4 page cover section. The setup should be in standard single pages or perhaps in readers spreads, again dictated by the printer (sequential page order, not imposed order).