I suppose something could be attempted on some operating systems of opening the DB handle in a wrapper process, setting it up to be passed through some IPC method, and launching your test script once that setup is complete. It seems to me that this would be very fragile and too clever to maintain.
Actually, that pretty much sums up DBD::Proxy. Not fragile at all, but precisely a piece of the core DBI package. And, for extra example code, see Coro::DBI (which cannot install via cpan only because the only release is a "developer" release though it has worked fine for me with the CB stats).