One SQL Server 2014 AG node down for 4 days - will it restart into AG?
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.