Actually Jack Harkness v1.0 played out that plot waaaay back when as a personal plot. Here's a link to the first day (http://time-agent.livejournal.com/13331.html"). And the next (http://time-agent.livejournal.com/13799.html). This went on for a few days.

And then she had to drop him, leaving him trapped in groundhog limbo.

Jack v2.0 rescued him out of it when she adopted him.

But as a plot, it was pretty cool