"Does a switch add a VLAN tag as a frame enters a switches access port?"
It might, or it might not. That's a proprietary architecture question. Such tagging is a requirement for frames on the wire. They are not required within the switch, itself.
"Or is it only added before a frame will traverse a trunk link?"
"traverse" as in an egress trunk port? Perhaps, perhaps not. Remember Cisco support a "native" VLAN on trunk ports, whose frames are transmitted untagged. Also keep in mind access ports with voice VLANs defined. Those frames are also transmitted tagged. Lastly, keep in mind "router" ports with subinterface using .q. I.e. those too can transmit tagged frames.
