Apart from HS2, trains from outside the region would still use the existing lines. Apart from the airport line, S-bahn frequencies may be 2, 3 or 4 tph on the current lines, but fast services are still enabled on the West Coast mainline, the Chat Moss, the Bolton line and the Trans Pennine mainline.
The Warrington, Atherton and Marple lines could still be served by heavy rail from outside the region, just as the T&W Metro enables 5 tph Metro between Sunderland & Newcastle calling at all stations, 1-2 tph for Northern services running on the same line between Sunderland & Pelaw. Those lines have already been called out for conversion for tram-train usage, meaning that heavy rail services will share the track still. Otherwise they would just be converted directly to Metrolink. It’s also important to note that ‘tram-train’ doesn’t mean the existing trams can use those lines and if a Metro tunnel is built (as Manchester wishes to do) ‘tram-train’ wouldn’t be the right phrase at all, given the service would be more like the T&W Metro.
In the case of the Warrington line, there are 14 miles of track between Warrington Central and roughly where a metro would enter the tunnel, where there are 7 intermediate stations, of which heavy rail could call at at least 2 of those stations. On the T&W Metro, there is 8 miles of track and 6 intermediate stations where there are shared running, where heavy rail doesn’t call at any of those stations. Therefore it is possible for both heavy rail and metro services to share the same infrastructure.