I have a locked iPhone (Verizon). Is it still possible to back it up on my iMac?

Hello, johnrpiano.

If the iPhone is locked, then it cannot be backed up to your iMac. It must be unlocked.

If you forgot your passcode to unlock the iPhone, you can reset it, but your data will be wiped and you will have to rely on a previous backup to recover your data.

If you forgot your iPhone passcode - Apple Support:

https://support.apple.com/en-us/HT204306

If the iPhone has been lost or stolen and the owner has activated Find My from their iCloud account, then the iPhone has been Activation Locked and cannot be used until the owner removes the lock using their account.

Activation Lock for iPhone - Apple Support:

https://support.apple.com/en-us/HT201365

Locked how?

If it's locked to Verizon as its carrier, then its irrelevant and can be backed up as long as you can access it.

If it's locked with a password you don't know or remember, then it cannot beg backed up.