I just tested this same setup in my lab and found the following:
Navigating to the IP of the router: Pass
Navigating to the IP of the APs: Pass
Navigating to the IP of the switch: Fail
Attempted to reach all devices on a flat network along with a VLANed network. What I didn't test was having the switch and my laptop be the only devices in the network and browse to "my.meraki.com". If the FQDN method is used then the page may flip between the AP or the router which ever device answers first.