From TechNet article Learn About Product Activation:
If activation does not occur immediately after the operating system is
installed, Windows 7 and Windows Server 2008 R2 still provide the full
functionality of the operating system for a limited amount of time, or
While the 30-day grace period has been removed since Windows 8 / Server 2012 and replaced with increased notifications and disabling personalization features, all the other features of the operating system still functions normally, so RDP even should be possible.
Licensed evaluation period of Server 2016 lasts 180 days. According to discussion on Spiceworks, a completely unactivated copy of 2008 and 2012 (& R2) runs 30 days (10 days for evaluation install) normally, and then starts shutting down once per hour. Probably 2016 does the same. However, that should be only theoretical as it doesn't take that long to get the actual licence. And it doesn't change that the OS is still otherwise fully functional.
Grayed out usually means there is a Group Policy affecting these settings. Review both your domain polixies and local group policies. I'd use Resultant Set of Policy MMC snap-in to see the affecting policy directly, regardless where the policy is set, as GPO inheritance may be complicated.
Expand Computer Configuration – Administrative Templates – Windows Components – Remote Desktop Services – Remote Desktop Session Host – Connections and check that Allow users to connect remotely using Remote Desktop Services is either Not configured or Enabled.