CDP is definitely one of the protocols that carries information about the native VLAN of a port, so if two ports do not match in their native VLAN setting and CDP is running, you will be getting warnings about native VLAN mismatch. This will happen both on access ports and on trunks. If you deactivate CDP, you will also deactivate the native VLAN mismatch detection mechanism provided by CDP.
However, Cisco's STP implementation, the PVST+ or PVRST+, uses a slightly extended BPDU format on trunks. Each PVST+ BPDU has a special record at its very end in which the originating VLAN of this BPDU is recorded. A receiving switch will compare this record from the BPDU with the VLAN in which the BPDU was received. If these two VLANs do not match then it means that the BPDU was originated in a different VLAN and was received in a different VLAN which is a typical sign of native VLAN mismatch.STP will react by blocking the trunk port for both its own local VLAN and the neigbhor's VLAN that was indicated in the BPDU. In this case, the connectivity in these two VLANs will be prohibited on this trunk to prevent possible switching loops. In STP, this is called PVID Inconsistency, and correspondingly, the port is put into PVID_Inconsistent state.
This check is not performed on access ports - on those, Cisco uses standard STP/RSTP.
So deactivating CDP will prevent it from detecting a native VLAN mismatch via CDP. Note that CDP never causes ports to become blocking - it always only reports its findings but never takes any action.
On trunk ports in particular, Cisco's PVST+ and PVRST+ perform its own native VLAN check, so even with CDP turned off, you can still detect native VLAN mismatch. Also, contrary to CDP, PVST+/PVRST+ will cause the trunk port to become blocking for the offending (mismatched) pair of VLANs. This check is not performed on access ports.
