A text can ‘read itself’, yes. As others have pointed out, read can be either active or mediopassive (which maps roughly, but not exactly, to transitive and intransitive uses). But if it used mediopassively, the text that ‘reads itself’ has to be the actual subject; otherwise, you would use say instead of read.
In your example, the subject it is a kind of dummy subject, which is a grammatical category that has quite a limited scope. In the case of read, a semantic subject is always required; but say can be used with either a semantic subject or a dummy subject. Thus, the following are all grammatical:
As the first page of the book says, … [semantic subject + say]
As it says on the first page of the book, … [dummy subject + say]
As the first page of the book reads, … [semantic subject + read]
– but this does not work:
*As it reads on the first page of the book, … [dummy subject + read]
There is moreover a semantic difference between the active and the mediopassive meanings of read. The mediopassive use generally does not focus on the content of the text reading itself, but the manner in which the text reads itself (see also Centaurus’ definitions of the two meanings). So even though “As the first page of the book reads, …” is grammatically all right, it is not something you’d be likely to hear, because the sentence is supposed to deal with what is actually written on the first page of the book, rather than how the experience or result of reading the first page of the book is.1
The mediopassive use of read is nearly always followed by an adverb or adjective that describes the effect that reading the text has (‘well’, ‘different’, ‘complicated’, ‘mellifluously’, etc.), or occasionally an object that is nearly always a direct quote (as in Centaurus’ example). So with a bit of modification, your example could be fine:
As the first page of the book reads so well, you might expect the rest of the book to be brilliant. Sadly, after just a few pages, the quality plummets, and the rest of the book is pure, unfiltered garbage.
But in your specific context, it would be much more natural to use the verb say or even the more formal passive construction be stated instead:
As it says on the first page of the book, marzipan is vile.
As (it) is stated on the first page of the book, marzipan is vile.
1 The ambiguity is of course also possible because as has two slightly different meanings here. In “as it says on…”, it basically means “in the same way as it says on…”; whereas in “as the text reads”, it means “how the texts reads”, more or less. The two meanings are very close to each other, but there is a difference in nuance.