How do I check Apple Coverage during maintenance?

I believe by checking coverage you mean your Warranty/Care+ coverage. As of this, by the scheduled maintenance they are probably referring to server maintenance, which would mean that you’ve got to wait until Apple finished that task. This just my interpretation though, which is based on general experience, I do not have any direct information about this, and other people seem to be presented with the error “system currently unavailable”, which does not match your report.

Apple reports on major services at the link below.

Apple - Support - System Status