As for now this is not possible. It might be implemented in a future release so I recommend that you file a feature request on a search feature.
Specifically how many thousand entries are we talking about and you are not seeing any entries at all? Is this a problem only in the Scheduler GUI or do you have the same problem in the Manage phonebooks aswell? Generally it should not be any limitation on the amount of phonebook entries, but would be interessting to know more specifically how many we are talking about?
In the TMS "FAT GUI" there is a Search feature implemented - no problem here but for the scheduler it is not.
For "Search Only" phonebooks you see just the phonebook name as a subfolder below "Phonebooks". No entries.
If it is a "Import to TMS" Phonebook the scheduler try to load the complete phonebook in the HTML source of the page. But with 100k+ entries it runs into browser timeouts. TMS is not usable for minutes...