Even then, your curbside recycling probably can't deal with random scrap metal. The one at our house only wants aluminum and tin containers. Anything else, you should probably give to a scrap metal recycler.
It doesn't matter what is theoretically recyclable. All that matters is what the recycler can handle.
So the rule of thumb is: there is no rule of thumb. Follow the local rules.
If you have metal, aluminum especially is a very valuable recyclable, so definitely keep recycling that.