We have a new cluster, all nodes are running 1.6.1. I'm planning on updating to 1.6.2 this week.
Is there any benefit to updating to 1.7.1 i.e. jumping track from 1.6 to 1.7 ?
Yep, delayed allocation is one big one.
This? That does look handy.
Drawbacks? Will my hair fall out? My bear turn gray(er)?
Elasticsearch has not been tested on animals, nor humans, so can't comment too much on your hair or beard 
I'd got with 1.7.1 (or 1.6.2) if you want to upgrade, see https://www.elastic.co/blog/elasticsearch-1-7-1-and-1-6-2-released