Interesting question. What preserves the cucumber or anything pickled is the acid, in pickling usually vinegar in some form. If the overall pH of the mix is low enough (somewhere in the low 4's) then bacteria generally can't grow. Some molds can grow in those pH levels but not bacteria so washing the cucumbers and keeping everything sterile is important. Water bath canning kills many molds but maybe not all. Refrigerating the food will slow the growth of many things, that's why recommended storage times are lower than water bath canned for refrigerated pickles. If yo do things different ways you get different results. Cucumbers are alkaline, a high Ph number. I'd think the commercial pickles went through some type of water bath process to get a seal and kill off some of the mold and such.
That's what I'm basing my opinion on. That's what mine is, opinion, I really don't know for sure. if the liquid was kept fairly sterile (don't use dirty forks or fingers to pull a pickle out) you probably haven't introduced many mold spores. If you kept it refrigerated what got in hasn't had a chance to grow much anyway. When you add the alkaline cucumbers to the acid liquid you raise the pH some, how much I don't know. That's probably going to vary some, to me this is the great unknown. Maybe you can use a good pH meter to get a reading? You could add more vinegar to lower pH but I don't know how much to add. I don't know how the commercial people do their water bath canning process.
I would not trust it for water bath canning and then storing the cans on the shelf at room temperature. Too many unknowns. I'd be more comfortable if they were refrigerated but I doubt you will find many Home Ec professionals that will agree with that, they tend to be very safe and go by strict recipes.
I understand your husbands curiosity but instead of using cucumbers I'd be more tempted to drop a hard-boiled egg in that liquid and refrigerate it for a week to give it time to absorb the flavors. See how pickled eggs taste. I bet those would be really good in pickled beet juice.