Does it work if my phone is locked?

Yes. Your Dropward opens your emergency profile on the responder's phone, not yours. Your phone stays locked and never needs to be touched.

This also means it keeps working if your own phone is damaged, out of battery, or lost in the accident. That is a good reason to carry your profile on something other than your phone: a card in your wallet or a keychain survives a phone that does not.

The information a responder needs lives in your account, not on your device.