I'm not convinced that the cumulative latency this would introduce into test runs is lower than the amount of time required to use brew or apt-get to install Postgres.
Installing a database server locally to run unit tests is something that has always annoyed me. 99.99% of the time when I'm testing things, I'm at a computer, hooked up to the internet, working on things--and I'm usually not all that concerned about an extra second of overhead.
I think the real benefit to this is that you can use the same DB harness regardless of where you're testing: locally, Jenkins, Travis-CI, whatever. This way, you don't have to write any code to make databases, check credentials, whatever, it's just a thoughtless process.
Locally I already have Postgres installed for development, and Travis does as well. I guess this might be useful for Jenkins on EC2 in the same AZ as Heroku Postgres, but the latency is still going to be painful.
tentd git:(master) $ time bundle exec rake
#...
Finished in 14.6 seconds
818 examples, 0 failures
real 19.10s
user 11.59s
sys 1.22s
tentd git:(master) $ time bundle exec rake TEST_DATABASE_URL=$(curl http://api.postgression.com)
#...
Finished in 15 minutes 0.49244 seconds
818 examples, 0 failures
real 905.67s
user 23.37s
sys 3.12s
$ time brew install postgresql
==> Downloading http://ftp.postgresql.org/pub/source/v9.2.2/postgresql-9.2.2.tar.bz2
######################################################################## 100.0%
#...
==> Summary
馃嵑 /usr/local/Cellar/postgresql/9.2.2: 2819 files, 39M, built in 3.2 minutes
real 190.33s
user 338.87s
sys 60.70s