One SQL Server 2014 AG node down for 4 days - will it restart into AG? We are planning one of our server rooms to be shutdown for 4 days. We have one node of each of our AGs in this server room.

It only just occurred to me that perhaps there may be an Availability Group tombstone setting (similar to replication), whereby an AG node once off line for a while may have a "use by" date and may not restart into the AG. I have looked a lot in MS doco and so far can't find anything that indicates an AG node might be timed out of the AG.

We run SQL Server 2014 SP1 on Windows 2012.
There is no tombstone in Availability Groups. However, one thing you need to consider is the mode your AG is in for the replica that is being taken down for 4 days, and how much log is going to need to be kept for that period.

An AG syncs up other replicas by sending the data written to the log of the database, if you are going to stop a replica for 4 days that could be ALOT of log space needed.

You are basically suspending data movement to that replica by taking it offline (or shutting it down). That is acceptable for a few hours on moderate loads, but when you get into days you need to remove that replica from the AG altogether. This is going to prevent the need to keep all the log data in the database log files for any database in that AG.