Kinda-sorta. They can use Google's services and pick and choose which services. That doesn't require Google Play Services or Google's apps. Google publishes the APIs for all their services, and anyone's free to get a developer account, generate API keys and create their own apps that access Google's services (as long as they don't abuse the services, of course). What they can't do is preload Play Services and/or Google's apps (which are copyrighted and not open-source) without an agreement with Google which is likely to require Google's core apps be the defaults. And frankly any suit by the OEMs like you suggest would die on the first motion to dismiss, since the locked bootloaders and locks apps are the OEM's and carrier's choice, not Google's. Google's quite happy with unlocked bootloaders and apps that the end-user can uninstall at will, it's usually the carriers who don't want their profitable deals disrupted by users removing the relevant apps. As far as forced bundling, they'd have to restrict the suit to just the all-or-nothing bundling of the apps without regard to Android itself and that's likely to fail on the grounds that none of the apps have monopolies (there's far too many alternatives to GMail, for instance). If they try to use Android as the underlying monopoly, the suit will fail on a motion to dismiss since the OEMs aren't required to bundle any of the apps as a condition of getting the ability to use Android.
The main issue is that the OEMs and carriers want to be able to sell access to the very lucrative search box on the phone to the highest bidder while still using Google's apps for all the other things that users expect access to like their contacts and e-mail, but Google's set terms that force them to do all their own work if they want to do that.