Possible to play without robots?

Yes.
Beat them before they get that far up the tech tree.
Otherwise, you may as well ask if it is possible to play without Bombers!
 
You can disable Gathering Storm: no more robots.

On a PC, you can remove them from the tech tree (or reposition their place on the tech tree) or adjust their strength by editing XML files.
Don’t think you can put these files on a playstation, though.
 
Some kind soul created a mod to disable rock bands. I was looking for a similar mod that disabled these childish, game-spoiling robots, but couldn't find one.
Will have to investigate the method in japanesesamurai's post.
 
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