If you are talking on AP1000 series then no WEB AUTH will not work as REAP AP always do local switching even when it is in connected status.
IF you have LWAPP converted APs they work as HREAP and WEB auth will work only when it is in connected satus but when it is in standalone status i.e when controller is unreachable state already authenticated clients will keep passing traffic but new clients will not be able to associate.
if i may make an additional query on this train of thought...
if the data will be switched locally, HREAP...then VPN connections would also be switched locally, correct? referring to the line diagram below, VPN connections will be terminated locally (not get on the LWAPP tunnel)