Availability Groups - Can async replica delay failover of sync replica?
When a Secondary (Node 3) is running in Asynchronous-Commit mode, Primary (Node 1) does not wait for a confirmation that Secondary has indeed finished writing the logs to its own log file. 
It will still wait for a confirmation from a secondary in Synchronous-Commit mode (Node 2) though.

Right after Node 1 will be finished writing the log record to its own log file, it will consider that the transaction has been completed and the client will be notified.

With Asynchronous-Commit mode, Secondary is considered to never be synchronized with the Primary. 
Secondary always remains unsynchronized and some lag with the Primary is to be expected although it will try to keep up and catch up with the Primary, 

Therefore problems or lags on a Secondary in Asynchronous-Commit mode won't impact the Primary.

Much more information are available on this MSDN page: Availability Modes (AlwaysOn Availability Groups)