Sure. You can do that.
Create the "generic" account and give it permission to whatever you need to. Set a password for the account and use Group Policy to make the autologon happen.
There isn't a stock Group Policy template to control autologon. A simple template would be something like:
POLICY "Auto Logon"
KEYNAME "SOFTWARE\Microsoft\Windows NT\CurrentVersion\Winlogon"
PART "Username" EDITTEXT
PART "Domain" EDITTEXT
PART "Password" EDITTEXT
END CATEGORY ; "Logon"
END CATEGORY ; "System"
Save that in an ".ADM" file, create your OU and GPO linked to it, and edit the GPO. In the Group Policy editor you'll need to right-click "Administrative Templates" and "Add/Remove Templates" to add this template. You'll find these settings under "Classic Administrative Templates".
Bear in mind that this setting will "tattoo" the registry of the PCs you apply it to. When you move them out of the OU they'll retain the autologon settings. Either remove them via script or relocate the PCs to an an OU with an "evil anti-policy" GPO linked that has the autologon setting disabled to un-tattoo them.
If you want some specific Group Policy settings to apply to the generic user account be sure you put that user object in the proper location and give it the proper group memberships, etc.