Elmer's is stronger than the material you are gluing- be it plaster, terra cotta or concrete- as long as you get a good clean break and you clamp/weight the pieces together nicely so there's no gaps- glue will not fill gaps and holes.
It will not affect the rubber, just don't apply so much it oozes out of the break and runs down all over the face, it doesn't take much to do the repair.
Here's a copy of the concrete bust I repaired per my previous post, it was 600# and 4' 1" high, hollow in the back with wall thickness about 2" or thereabouts;
While this is an extreme example of whta Elmers glue has held together, I used Elmers by the gallon back then to repair broken terra cotta architectural sculptures.
The whole side of the original - shoulder to the nose and down to the base was broken, you can see the left corner on the base where it had hit- the crack went up through there to the nose and then over to the top of the shoulder.
One test with Duco cement on something else was a failure- it lasted a week and the part I glued with it fell off.