Say I have a Unity WebGL application on my website; would I be able to get the real time and date of the server on which the website is hosted?
I don’t know if there is a unity want to do this or not. If there isn’t then you’ll probably want to look at building a plugin: Unity - Manual: Interaction with browser scripting
Yes, you are “able” to get that information, but you have to write a small php script which does return that information to your application on request.
What PHP function you need can easily be found on the net. If you want to use the time / date in Unity it might be a good idea to pick a format of the date / time string that the .NET DateTime type can read in.