Is rebate/rabbet joint with glue only strong enough?

If I use a rebate to joint 2 boards together, is it mandatory to use screws/nails to support it or will the glue alone hold just fine?

The glue alone can be perfectly sufficient for a joint like this. Whether it is in practice depends on various factors, including:

• the loads it will be subject to, especially any shock loads¹;
• movement stresses (movement of the completed item, not wood movement);
• the quality of the joint prep (flatness of the joint surfaces and the final fit);
• the material used;
• and how good the glue-up procedure is².

If in doubt it is a good idea to reinforce in some way. Erring on the side of strength is rarely, if ever, a poor choice in furniture making. Even a few brad nails or some dowels can add significantly to the final strength of box structures like this. Toenail/dovetail the brads or dowels to maximise the reinforcement³.

If you are reinforcing the quality of the joints is less critical, but don't use this as an excuse for sloppy fit :-) However, if you do end up with one or more of the joints fitting poorly it would be a good idea to switch from using PVA-type woodworking glue to an epoxy since the latter have good gap-filling properties and the former do not.

My main concern is the fact that (to my knowledge) end grain doesn't provide much strength when glued.

A rebate joint isn't a simple end grain joint like a mitre is, so some of the (legitimate) worries about end grain glueing poorly don't apply. More on the general topic in this previous Answer, What are the different grain directions, and how do they affect joint strength?

---

¹ E.g. legs being thrown up on to the top, a child sitting on it, or it being moved around by biffing it with the shins.

² Surfaces should be freshly worked, and if not refreshed with a light sanding just before glue goes on. Enough glue must be applied to fully wet both surfaces, and then sufficient clamp pressure applied to squeeze out all the excess.

³ I generally install any through-dowels with a slight lean anyway, just a few degrees off square. And once you use a pair at opposing angles you end up with a great deal more added strength than if they were both installed at 90°.