It is possible - however in order for your code to read permissions for any users running a vault extension or through iLogic/Inventor Addin - you must assign the Administrator User Read Permission to all users. I achieve this in my vault by making a custom Role that I add to all groups.
From there you can look at the Autodesk.Connectivity.WebServices.AdminService class in the Vault SDK.
Once you get the vault connection object you can get to the AdminService.
I have this for getting and checking if the logged in user has permissions.
userperms = mVltCon.WebServiceManager.AdminService.GetPermissionsByUserId(mVltCon.UserID).Select(a => a.Descr);
if(userperms.Contains("Link Create")) { ...
also
var usr = mVltCon.WebServiceManager.AdminService.GetUserInfoByUserId(mVltCon.UserID);
if(usr.Groups.Select(a => a.Name).Contains("something")) { ...
There are also methods for looking at groups or roles.
I recommend using try/catch when accessing permissions otherwise you can get errors if the user doesn't have read permissions.
