Yes.
There's no documented enforced limit (that I could find) on the size of the pasteboard. However, everything is finite. If you copy too much stuff to any pasteboard (whether it's the general pasteboard, the Find pasteboard, a drag pasteboard, or any other), you'll either hit an undocumented limit or you'll drive the system into paging hell. (Even that last part isn't really guaranteed; the pasteboard uses RAM the last time I checked, but it theoretically could write to disk instead either now or in the future.)
If you plan on copying a large quantity of data, I suggest promising it instead. How you do that depends on whether you're using the older type-and-data-based API, or the newer item-based API. It's more work, but it means you'll only need to bring in that data when the user pastes it somewhere.