Will apple erase my info from my Mac

If you're truly concerned about erasing data, do it yourself. Since you're wanting to recycle your Mac, then you can just erase it and not even bother re-installing MacOS.

It's very easy to do.

With your Mac powered off, turn it back on while holding down cmd->R. That will get you into the utilities menu.

Select "Disk Utilities". Select your storage device on the left side, and click the "erase" option on the right. You will get a panel with format/wipe level options. The base is usually good enough, the other more secure wipes are better, but just take longer.

I would not trust anyone else to ensure my machine has been wiped out.

since it's headed to the recyclers, you could always open it up and physically remove the drive before taking it to your local electronics recycler. i would personally do that, especially if it has a mechanical drive. you can go to OWC's website and find the hard drive install video for your particular iMac to learn how to take it out. and you don't even need to be gentle disassembling it if it's going for final disposal.