Restore transactional replication subscriber database to different server

Hi, 

Our publishers, distributor and subscribers are on three separate servers and SQL Servers respectively.

Our subscriber and system databases are unavailable due to a SAN failure.

Is it possible to restore backups of the subscriber and system databases to a brand new instance without losing the pull subscription to the existing publications?

I would like to restore all subscriber and system databases to a new SQL Server instance on a different server without losing access to the transactions building up on the remote distributor.   

Thanks