Macbook Pro WiFi hardware sporadically malfunctioning
My thinking is that the cable connecting to the airport card was
  damaged when I dropped the laptop. Does this seem likely?


You need to diagnose the issue and without actually putting "hands on" the unit itself, everything's just a guess at this point.   That said,  there's nothing in NVRAM or in power management (SMC) that resetting both/either will solve.

The "No WiFi hardware installed" means the hardware isn't being detected by macOS. 

There are three possibilities:


It's has a loose connection.
The airport card is failing (possibly coincidental with your drop).  
The connector is broken


The first one is easy to diagnose/solve; simply disconnect, ensure that connections are clean, and then reconnect.  

If the airport card has failed, you need to replace it with new Airport Adapter.

Finally, if the connectors are broken, you can either replace the cable as you initially thought or if it's on the logic board side, you will need to have the logic board repaired/replaced.