Is a table without a primary key normalized?
If a relation does not have any candidate key (and the primary key is just one of the candidate keys), then it can have duplicate rows, so in fact it is not a relation! (since relations are always sets).

In that case, it is more correct to call it a table, not a relation, as you did in your question, and note that several RDBMS in effect can manage not-relations, allowing tables without any constraint of uniqueness, even if this case is very uncommon, and produces problem (anomalies) when operating on the data.

But in this case talking about normal forms is not appropriate: all the normalization theory is based on the fundamental assumption that the objects of interest are relations, not multisets. In fact this theory is based on the (somewhat discussed) Universal Relation Assumption, that assumes that all the relations of a database are a subset of a projection of such relation, that contains all the attributes in every relation. And that object is in fact a relation (i.e. a set), not a multiset.

The fact that, when talking about data of the Relational Data Model, sometimes we exchange the two terms, tables and relations, does not means that they are actually synonym, and this difference is fundamental when we talk about normalization theory. Remember that in the books, when some normal form is introduced, it is always said something like: 


  A relation is in xxx normal form if...