If you drug anchor, the extra chain may or may not help. What anchor were you using and what was the bottom type?
Safety wise Martin id correct--50' of new chain is stronger than a splice link in the old chain. Being that the C Dory is rarely loaded to significant anchor loads there are several ways to add a chain link for joining the chain--but never as strong as the initial intact G4 hi test chain.
One is a "soft link" using Dyneema or similar product. I have a couple of Dyneema shackles (one came with the boat, another I made). My concern would be pinching and abrasion--I would want to inspect the link regularly.
One trick I have used is a peen chain link. I put JB weld on all mating surfaces and then peen over the nubbins. I have never load tested this, but it probably will hold anything like what the average C Dory is hit with.
There are other connecting links: But none go all that well thru the windless:
A carabiner or spring steel link is just not strong enough.
I carry several rodes on my boats--on the current boat, I kept the main anchor rode as a stern and back up--and replaced it with 300' of 8 plait and 50 feet of G4 1/4" chain.