IME this may not do anything at all, but it’s worth a try if it’ll give you piece of mind. If you’re doing it for durability’s sake, you want a filler that’s flexible and strong, like the original rubber itself. I’ve tried repairing cuts in the tread of tubulars and clinchers with superglue because I’m super freakin cheap, with mixed results. The super glue on the tubular just wore off, but that was more of a surface cut in the tread than a deep cut into the tire plies. I’m beginning to think that the best solution would be to put a small piece of duct tape on the inside of the tire in the vicinity of the hole. This would only really be necessary if the hole goes all the way through the tire, and would only prevent the tire from somehow getting pushed toward/out of a small hole in your tire. A 1/16th cut that doesn’t go through the fabric layer is not even worse messing with–the rubber doesn’t do a whole lot for the tire from a structural standpoint, and the structural damage from a cut that small has to be minimal, so filling in a hole in the rubber with adhesive shouldn’t theoretically improve or detract from the structural properties of the tire. I can’t see rubber cement adding a whole lot of durability to the tread either.
That said, I had a hole in my tire that went all the way through, about the size you’re describing when the tire isn’t pumped up, and I did successfully “patch” it with super glue and duct tape. I’m not sure it did anything more than give me piece of mind, but I got many many more miles out of that tire before general wear to other parts of the tire led me to “retire” it. It may be my patch job worked, it may be there was nothing wrong with the tire to begin with. Either way it was rideable afterward.