Can Uber pick up at Fort Lauderdale Airport?

Not in the past, but now they can. Special pickup areas have been designated.

Ye, Uber and other rideshare services can now pick up at Fort Lauderdale Airport.  This was not the case a few years ago, where originally, anyone could, and later they banned all rideshare services from picking up. (Dropping off was okay.)

Since then, there's been a proper policy set in place and a special designated areas have been designed.  See here for more detailed pickup policies.

Uber, Lyft, Taxis, Limos, and others at Fort Lauderdale Hollywood International Airport (FLL) 

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Uber Driver, CEO of TaxiFareFinder and Unleashed, LLC