Your fix will probably fail for something supporting a large load (like a hinge). You might be ok if you're just holding a strike-plate. As others have noted, "wood glue" (I'm assuming you mean alphatic resin) is not good at gap-filling (like foaming urethane glues) nor at having good shape-holding strength (like something like JB Weld). In fact, AR glue initially cures to be rather soft, and then becomes hard and brittle.
My understanding of how AR glue works is that it temporarily softens the natural binder (that the tree created) between the wood fibers. This means that, under adequate clamping pressure, the fibers from the two wood pieces will actually mesh with each other. Done properly, this will leave a glue joint which is stronger than the pieces of wood, themselves. As hard as it may be to believe this, I've personally witnessed this... several times. Anyway, the point is: a good wood-glue joint doesn't use the glue to provide any "body", and, as such, a good joint will squeeze out a majority of the glue you apply.
As you might have surmised, in order for AR glue to do this, it is important to: 1) get as many wood fibers from both pieces in contact with each other, and 2) get pressure on them so that they intermingle. This is why you see woodworkers obsess over getting really flat, smooth joining surfaces (because any roughness just creates "pockets" of glue which don't help you), and they go to great lengths to get tons of clamping pressure everywhere (lots of clamps and using cauls to distribute that pressure evenly).
With that all out of the way, if you're just using the screws to hold the latch faceplate or the strike plate in, you may be ok with the technique you used. If you were doing that with a hinge, I wouldn't think it would hold up even a few minutes.
So... what are some other things you can do? Here they are in order of most-correct to the more under/over-doing it.
- The "dowel" trick. Some others have mentioned using toothpicks or a golf tee. These are all variations of the notion of "completely repairing the hole to be a solid piece of wood and re-drilling the hole". I don't think toothpicks are optimal as there will be gaps between them (and gaps are bad with AR glue) and golf tees are sub-optimal because they're painted (inhibiting the function of the glue). Instead, go get some wooden dowel rod of a diameter a little bigger around than the diameter of the screws you're going to use later (maybe about 1/8" greater dia) and cut off a piece to serve as the plug. Sand/file one end of the plug so that it has a little taper/bevel to help shoehorn it into the hole. Then, pick a drill a little smaller than that diameter and drill out the stripped hole so that the plug fits really snugly. Try to use a sharp drill and not drift your hand too much while drilling, as we want the hole to be smooth and of constant diameter. (Note: if the door/jamb you're repairing is somewhat deteriorated, then choose a larger hole/dowel to get to better wood). Now, slather wood glue along the inside of the hole and along the plug and tap it into the hole. The snugness of the hole is going to provide some clamping pressure between the faces. After the glue cures (about 12-24 hours), you can drill pilot holes for the screws. Use pilot holes of the same diameter (or just a little smaller) than the shank of the screw. You can do this either with calipers or by holding the drill in front of the screw to see how much of the screw shank is visible. This will prevent the screw from trying to crack the plug and/or surrounding wood. Lastly, in order to keep your screw holes from getting stripped in the future, this is the best way I've found to prevent wood/plastic screw holes from getting stripped from repeated removals/insertions of a screw: Rule 1: Use the same screw, when possible. Rule 2: When re-inserting the screw, apply light pressure while turning the screw counter-clockwise (i.e. the "remove" direction) until you feel the screw "drop into" the existing threads in the wood/plastic. Now, you can start driving the screw. This guards against cutting a new set of threads, which, done enough times, would completely bore out all of the wood used for holding the threads. Following these two rules, I've been able to remove/replace screws in wood 5-6 times without ever stripping the hole. (Note, if you do this method while anyone is watching, they'll call you an idiot because they think you don't know which way to turn a screw to drive it).
- Just go to your local hardware store and find longer screws of similar gauge and countersunk head.
- I've seen home-improvement stores sell little short tubes of perforated metal which resembles a cheese/potato grater. You stick those into the hole and the perforations grab onto the hole and then the screw bites into the metal. These should work if you're in a hurry and don't care about being able to remove/re-insert screws later.
- If you're really crazy, you could get threaded inserts. These are brass (or stainless steel) sleeves which are threaded for wood on the outside and have machine threads on the inside. Drill a large hole out of your jamb, and drive the threaded insert in. Basically, you'd be installing machine screws into your door jamb. Guaranteed to never strip, but you'd also take home the trophy for most over-repaired home repair job of the week.