It is possible to write a crontab-like service for the BlackBerry. Indeed, you should be able to pull off a similar service on any device which supports background tasks, of which BlackBerry is one.
On a mobile platform, however, the issue isn't so much as to whether you can get a crontab-like service to work, the issue is what is that crontab task going to do once it runs on its schedule? Mobile platforms, even those that allow background tasks so you can implement a crontab-like facility, aren't very open when it comes to your process accessing other processes, especially system-owned processes.
So, while, yes, you can implement a crontab on some mobile platforms, the actions performed by the scheduled task would be limited; probably to actions within a small set of allowed/open system facilities.
You can find more information about programming for the RIM BlackBerry line of devices (they do allow background processing), from the following page:
http://na.blackberry.com/eng/developers/