A gallon of pond water will be a drop in the bucket. Plus if there's any parasite/disease activity going on in the old pond, adding it to a new pond that isn't biologically stable could cause some problems, albeit unlikely. I wouldn't do it when the alternative is much simpler.
To counter one comment about 'off the shelf' bugs not containing the same indigenous populations... I'm not sure about other products, but we use non-gmo, natural and indigenous bacteria that thrive best in those environments and are found everywhere good water features are, but in concentrated form. Other manufacturers use different/modified strains and I can't attest to their effectivity, but I know some work, but most don't. Also, many off the shelf options don't contain enzymes (they rely on the bacteria to produce their own), making it more challenging for the bugs to do their work, ESPECIALLY in ponds with an existing organic load. The enzymes go ahead of the bacteria, breaking down the organic material to make it easier for the bacteria to digest the nutrients and get a leg up.
I hope that helps.