Are there any advantages of using rules-based approaches versus models for detecting spam? Suppose that we have unlabeled data. That is, all we have are a collection of emails and want to determine whether any of them is spam or not. Let's say we have $1,000$ rules to determine whether a particular email is spam or not. For example, one rule could be that a sender's email address should not contain the text  no_reply . If an email does contain this text, then it would be classified as spam.
What are the advantages/disadvantages of a rules-based approach for detecting spam vs. a non-rules-based approach/unsupervised methods for detecting spam?
Would there even be a point in constructing a non-rules based model given that we already have a rules-based model? Could we use the rules-based model to create some labeled training data and then apply supervised techniques?
Yes, there would be a point. Assuming your rule set is accurate, then you can use data classified with it to train a model. This model can be expected to be more robust and properly categorise emails that your rule-set will not handle.

Why? Machine learning algorithms generally work on features, and identify relationships between those features that lead to a classification decision. A human rule author basically does the same, but they might not notice subtle relationships; a good ML algorithm, however, might pick those up.

So you could have a hybrid model, where you first use your rule-based classifier, and anything that does not get classified is then run through the ML classifier.