How do I check whether this user is anonymous or actually a user on my system?

An Alternative to

if user.is_anonymous():
    # user is anon user

is by testing to see what the id of the user object is:

if user.id == None:
    # user is anon user
else:
    # user is a real user

see https://docs.djangoproject.com/en/dev/ref/contrib/auth/#anonymous-users

You can check if request.user.is_anonymous returns True.