No, the replacement is probably not valid.
The word periodical refers to a publication that is published as a series of issues. The relationship is similar to that between a deck of cards and an individual card.
You could say something like
A new issue is published every month.
The issue is published every month.
What's happening is that the definite article the is being replaced with the indefinite article a to indicate that you could be talking about any issue and not a particular one. The adjective new is optional here but sounds better to my ear. It could just be
An issue is published every month.
Here, we switched to an which is identical to a in meaning but precedes words that begin with a vowel and some1 words that begin with 'h'.
1 Technically I think it precedes all words that begin with an 'h' but that's sort of a dated rule in actual usage in the United States.