No, because the HSM in the token has a program that takes data from the application, signs it with the private key in the HSM and returns a digest to the application as part of the signing process. The whole point is the private key is not available outside the HSM so can not be copied.
The HSM/token can be used remotely only if the data to be signed is passed to the PC/server with the HSM, and the digest returned to the originating PC.
Angus