Not a lot of people seem to be using it, no.
Andrew Franklin did some work recently on updating H2's support for the PostgreSQL JDBC driver in the following issues:
481, 472, 477, 473 and 475.
Judging by the comments in
https://code.google.com/p/h2database/issues/detail?id=472
he seemed to think he had added support for versions of PostgresSQL from 8.1 to 9.2.