The chemicals are hardly similar. Caps are Aluminum and Borax. I don't think either is used in any common battery. I think you just clog-up the process.
You could pull the guts out and rinse the electrolyte off the metal. Then rinse your hands vary well! (The borax is just itchy but some minor spices are bio-active). What do you do with the rinse water? Your sewer service can't refuse a few gallons but they have no real way to break the stuff down (it's not organic). _I_ would prefer not to put too much in my septic tank. I don't want to stun my poop-eating bacteria. (Supposedly I do not put the mildly alkaline condensate from my gas burner in the septic either.)
Unless you are recycling modern welders, you don't have enough Aluminum caps to be worth the drive. Or rather: you can find more Bud beer cans on the drive to the recycler than Aluminum in your caps.
"bulk iron" is a thing. $10 or $20 a ton. This is typically cars with dirt and crap and some more valuable metals (copper, aluminum, vanadium) too small or alloyed-in to be worth the separating. You can suspect that where this comes together in trainload lots, and the iron melted out, someone will be skimming the pot for nonferrous metals and sending them to an appropriate buyer. That 1971 Firebird on blocks in the neighbor's yard? He's never really going to fix it. Throw your caps in there (after dark). When, eventually, his daughters clear-out the estate, it will go to the scrap-metal yard.