Yes. You can bypass the routing mesh, so that when you access the bound port on a given node, you are always accessing the instance of the service running on that node. This is referred to as host mode.
To bypass the routing mesh, you must use the long --publish service and set mode to host. If you omit the mode key or set it to ingress, the routing mesh is used.
The following command creates a global service using host mode and bypassing the routing mesh.
$ docker service create --name dns-cache \
--publish published=53,target=53,protocol=udp,mode=host \
--mode global \