No. Not with Server.app (with the exception of pushing profiles if you use Profile Manager (has additional requirements including a valid SSL cert, fixed IP preferred on WAN, push certificate, etc.)). Many of the other tasks are possible with Apple Remote Desktop and some ingenuity. But... you are limited to managing devices only while on the LAN. Management of remote devices would not be possible. If all you have is iMacs or minis and nothing leaves the LAN, you can use ARD.
If you are trying to support a mobile fleet, you should be looking at an MDM solution like Jamf Pro.
Hope this is helpful.
Reid