you're quite right in that even the same operation can work quite differently on the same db engine but on different architecture. the db engine vendors do try to make things as portable but they're never 100%.
on a side note in regards to different db engines, it's interesting to see some not so minor SQL standard implementations by the different vendors. some of this is documented in Joe Celko's book "SQL for Smarties"
in terms of further developing your test suite...maybe it could be made more black box like by having a config. As for checking whether a db engine exists on a machine or such, you could run basic sanity check before running tests proper. The sanity check typically written in "eval" style defensive coding to connect to db etc.
or maybe i'm missing the point entirely?