I can check if user is Domain Administrator by the following lines of code:
using (DirectoryEntry domainEntry = new DirectoryEntry(string.Format("LDAP://{0}", domain)))
{
    byte[] domainSIdArray = (byte[])domainEntry.Properties["objectSid"].Value;
    SecurityIdentifier domainSId = new SecurityIdentifier(domainSIdArray, 0);
    SecurityIdentifier domainAdminsSId = new SecurityIdentifier(WellKnownSidType.AccountDomainAdminsSid, domainSId);
    using (DirectoryEntry groupEntry = new DirectoryEntry(string.Format("LDAP://<SID={0}>", BuildOctetString(domainAdminsSId))))
    {
        string adminDn = groupEntry.Properties["distinguishedname"].Value as string;
        SearchResult result = (new DirectorySearcher(domainEntry, string.Format("(&(objectCategory=user)(samAccountName={0}))", userName), new[] { "memberOf" })).FindOne();
        return result.Properties["memberOf"].Contains(adminDn);
    }
}
More details here
But when the Domain Controller is turned off, or its off-line (without any connections), I get the following error:
The server is not operational.
at System.DirectoryServices.DirectoryEntry.Bind(Boolean throwIfFail)
at System.DirectoryServices.DirectoryEntry.Bind()
at System.DirectoryServices.DirectoryEntry.get_AdsObject()
at System.DirectoryServices.PropertyValueCollection.PopulateList()
at System.DirectoryServices.PropertyValueCollection..ctor(DirectoryEntry entry, String propertyName)
at System.DirectoryServices.PropertyCollection.get_Item(String propertyName)
Is there an ability to check if user is Domain Administrator with turned off Domain Controller?