They'll likely cancel your whole subsequent itinerary if you don't fly the first, or any preceding leg.
Try fitting in a red eye flight. My sister once had to "overnight" on her way back to LON. She was thinking of overnighting in YYC. What i had her do was take the red eye to YYZ on one night and then connect onto the morning flight to LHR the next morning. A 3 hr layover in YYZ but it did the trick.
[This message has been edited by terenz (edited 09-04-2000).]