ElasticSearch Downtime From Closing and Opening Index

Question

I'm managing an ElasticSearch cluster and I need to add an analyzer to one of my indices. The particular index I want to update is a bit more than 3TB. Will there be an excessive amount of downtime associated with closing and reopening this large of an index to add the analyzer? The documentation doesn't seem to say anything about the processing required to close and open an index.

I have done many rolling restarts and the shard recovery is pretty quick, but I'm guessing that closing and opening an index cannot be done one node at a time with a rolling restart.