No. Only the VLANs in the VLAN allowed list will pass. In fact, the Cisco security best practices recommend not using VLAN 1 (the default VLAN), not using a native VLAN, and restricting the VLANs allowed to only those actually needed on the trunk.
To that end, you can leave VLAN 1 as the native VLAN and not include it in the `switchport trunk allowed vlan` command. Also, disable the VLAN 1 SVI on any switches.
You should also use the `switchport nonegotiate` interface command on the switch interfaces to disable DTP that can negotiate between access an trunk for the interface.