I think you could do that right now as well. In the 3CXPhone app you can go to the menu and then "Hot keys" menu and enable the "Copy number to clipboard" and select a key combination (I have Ctrl + F11).
Now once you highlight a number somewhere and you press the combination, this number will be copied and pasted into the 3CXPhone app, so all you need to do to dial at this point is press the Enter key.
Sortcuts work very nice, but only with power users.
I think I did setup some TAPI browser plugin once, but I am not sure, if it would still work on V14.
A browser pluging would be a more direct and visible way to offer this functionality.