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No, a native VLAN is the term for an untagged L2 packet on a L2 trunk. Basically, for an untagged trunk frame, what to assume the VLAN is for that frame.
By default, Cisco switches assume VLAN 1 for untagged frames, but this can be changed.
Telnet access just requires the switch's management IP to be on a VLAN/subnet that can be reached by other hosts. It could be on any VLAN.