Well realistically we should see on occasion Jack coming across references to the Doctor. It does depend on what time period Torchwood is set in as well - I'm placing money on their first season finale happening just before the events in TCI - they do mention that Torchwood had lost the majority of their staff and that was why it was taking them so long to get the weaponry online.

It's going to be interesting to see how they do it. I mean, if Jack wants to hook back up with the Doctor, the first bloody thing he's going to do is go look up Jackie Tyler - and then get a hold of Rose through those channels. (Unless of course he does that and it's pre-2005 series and realises that she hasn't met him yet) Which is a bit of a bummer because I just had this heartbreaking mental image of Jack arriving on the scene in TCI just after the TARDIS leaves again...