We have masonite siding and are having a few boards replaced. The contractor we are talking with wants to use metel drip edge to replace the boards. Is this common practice and if so, is an exact match possible or will this look like a train wreck?

Drip edge is not any sort of replacement for siding but is used to direct water away from the siding to reduce future water problems. Get the contractor to show you what he is talking about and see if you like the way it looks. To me it looks neither good nor bad, but functional. It can help your siding last considerably longer if properly installed, but masonite is relatively inexpensive to replace and you're the one who has to live with how it looks, so it's your call.

UPDATE: After giving it more thought, I might consider using a piece of drip edge for a long narrow run at the very top of the wall, or under a window. Long narrow pieces of masonite are hard to handle, easy to break, and generally require more hands to cut and install, but if I were doing the job myself and the gap was an inch or less, I would consider the drip edge. .......maybe.

Not quite sure what you mean by metal drip edge?
If your talking about sheet style siding like plywood, and the seams are butting against each other then yes flashing is needed where the seams meet. But if your talking about clapboard siding where one edge runs under the next, then there is no reason for this flashing.
Flashing is used to divert water out or away from where it will do damage. If the house has had no flashing in the past in these areas and your not butting the edges of the siding against each other. There is no reason to have flashing installed.
As far as matching what is there. Masonite siding has changed very little in design over the years. They have added some new patterns but what was installed in the past is still available at your better lumber stores in your area.