[AC Question]

I want the phone to be unreponsive to someone picking it up but still accessible remotely.

[ManiacJoe]

I doubt you can do that.

For the remote connection to succeed, you will need to unlock the phone then "accept" the remote connection (or create the connection from the phone).

After that you may be able to lock the screen, but it is still going to be completely responsive.

What is the goal you are trying to achieve?
Which phone?
Which version of android?
Which carrier?