I'm pretty sure the signalling on the Southport line can support more than 4tph (at peak hours there are extra trains slotted in around the base 15 minute frequency) so as long as you're prepared to accept a slow journey pathed between Merseyrail stoppers it would be perfectly possible to send a railtour that way.
The key issue would be what rolling stock is cleared for that route; I've seen a variety of locos on engineering trains, but would a Mk3 coach be OK?
I have a memory that at some point (late 1990s I think) a railtour using a Southern DEMU made it to Southport via the Bootle branch and the Northern Line. I'm sure I saw a photo online showing the unit passing through Birkdale.
However, I can find no photographic evidence of that train now, and the Hastings Diesels website makes no mention of it, so maybe my memory is faulty. If anyone could confirm that I'm not going mad, that would be great.