Are industry based labs interested in Searchable Encryption?
Searchable Encryption strikes me as a neat solution to a problem that doesn't arise all that often.
One place where you might think searchable encryption would be useful are encrypted databases; you encrypt one of the fields within your database, and then the encryptor can issue searches for specific values of that. However, what the untrusted searcher ends up doing is running the 'test routine' each time for every entry in the database (to see if that column is a match or not) - if we're talking about a database with millions of entries, well, even a cheap test function run millions of times is no longer cheap.
If you can propose a searchable encryption algorithm that allows for such a database-wide search in sublinear time (or linear time with an extremely small multiplier), someone might find that useful (then again, they might not).
Will doing a PhD in Searchable Encryption help my join industry based research labs?
I suspect that crypto is somewhat different than other fields. In other (possibly more mature) fields, one might expect future work to be in the same subarea as your PhD; for example, if you were interested in doing professional work in numeric computation, a PhD in topology might not be considered relevant. This is less true of cryptography, where is considerably more crossover.
On the other hand, if you were looking for a sellable work, I would suggest that you might want to look into cryptanalysis (and it doesn't really matter of what, as long as it is not too obscure); a concrete attack against an in-use cipher or protocol will always be taken as significant, while proposing yet another cryptographical primitive might not be.
How active is the field of Searchable Encryption?
That is something you should take the time to find out. After all, if you were to work on a PhD in Searchable Encryption, your first task would be to go through an exhaustive literature search in the area. While going through each work with the required thoroughness will take a while, just finding the relevant literature should not. And, the amount of recent published work would certainly tell you how active it is.
