I've done exactly what you describe but with bone-handled knives which
have a sort-of tang on the end of the blade. It worked perfectly. If,
on the other hand, the knives have been through the wash/dishwasher
too many times, it is possible that too much of the animal glue has
been washed out for a simple repair like that to be any good. I'd try
it and see what happens. If I had to reglue it, I'd be inclined to use
animal glue because I work with the stuff on a daily basis anyway but
if you don't (work with the stuff on a daily basis) you might want to
enquire after alternatives.
Nick