I think you need to answer a couple of questions first:
What do you expect to happen when you serialize the DB connection? Should the DB connection be closed? What should be stored in the serialized data structure?
What do you expect to happen when you de-serialize the DB connection? Should the connection happen immediately? What about waiting until the first query because you may not actually use the DB connection at every given de-serialization.
There are some further concerns:
Should passwords be stored? If so, how?
How should DBI connections using DBD::Excel or DBD::CSV work?
What should happen if you de-serialize the thing and attempt to use the DB connection on a box that doesn't have the right things installed?
And I'm sure that I'm missing some concerns. In other words, serializing stuff that uses external resources is non-trivial. I've run into the same problem with DBM::Deep and I don't have a really good way to solve it as of yet.
My criteria for good software:
Does it work?
Can someone else come in, make a change, and be reasonably certain no bugs were introduced?