Consider using a keyboard-mouse macro. If you are using a proper gaming mouse and keyboard you could program a simple conditional like: IF Left-Click then Enter Character 'A'
Thus, every time you you left-click you would automatically enter attack move mode if you have one or more units selected. But as Nick122 has warned, there may be unforeseen consequences such as attacking a gas refinery that you intended to harvest from if you are selecting SCVs, although when you mine minerals or gas you usually right-click... but still...
If you are serious about this I recommend programming a macro like the one I described, and testing this for yourself if you have a gaming keyboard and mouse which have this as a native feature. Otherwise, you would need to get third-party macro software for your mouse and keyboard which would need to run in the background while you play Starcraft II.
My verdict: an interesting notion but not worth the effort. If you want to optimize your game-play there are other useful things you can do. I play Zerg and have set my space-bar key to rotate between hatcheries for faster injecting, for example. If you do test this out, post the results here. I for one, would be interested.