Of course, something else has to happen for PHP to run in the first place.
If you don't have cron access (and you should - check w/your host), you can work around it.
I used to have an include on one of my pages that looks into the db for a target time and if it is within 1 day of the target it executes another script for me (to send follow up emails) and sets a new target date.
I would put this on a webpage that gets about 20 visitors a day or something - you don't want it on a homepage or a page that gets 1,000s of hits a day - too much overhead.