Interfaces on WLC are Layer-2 and you need external L3 device for routing.
it is like SVI on switch but no Layer3(however it does some L3 for out of band management using static route config on wlc). With atleast one configured tagged vlan on WLC to its connected switch physical interface should always be trunked.
every active ssid(layer-1) needs to have interface/vlan(layer-2) mapped to it, without that it is an switch port with no vlan(including native) attached to it, however WLC mandate to select interface for all wlan created(default is management).
you should be able to ping the WLC interface ip, if the w.less client(with ip) connected wlan has same interface mapped to it or other interface with inter-vlan/L3 access.
Purpose of management interface is to carry AP traffic(that includes all wlan traffic), wlans can also be mapped to management interface(should avoid for security reasons), Dynamic interfaces mapped to wlans uses that subnet/vlan to talk to wired infrastructure from WLC to its connected switch using dynamic interface mapped physical interface. there is no wlan's mapped vlan id between wireless client until ingress physical port of WLC via AP, it is only wlc that tags the packet before forwarding to its upstream infrastruture device.