Yes, that is why, if you use tagged management VLANs, the APs at the far site will have to be set by hand to use VLAN 200. Or maybe you can change the VLAN 200 in the switch to be the native one, untagged, in which case, it really doesn't matter. The AP can think it's suing VLAN 1, as long as it is untagged, it will work the same.