I dislike all forms of business spam which is what is happening in this case but it's exceptionally bad when it's out-of-the-norm spam.
By that I mean we all expect random email and certainly some snail mail to come in. We don't like it, we may negatively associate the company with it, but we aren't surprised either.
When something is done outside the parameters of what's excepted and requested it becomes a target and the response to it is terrible. Take text messages for example... there's only a handful of marketing promos floating around out there but when someone gets one you know all about it and those are from random scams, not identifiable companies.
People who like a page, especially a small page, tend to be the most local advocates or at least engaged customers. Thus when you cross the line to them you are very literally upsetting the people who defend you. This is made worse now that Facebook has become as mainstream as one can get. The bar is set, people know what to expect and crossing that line is insanely obvious.
There are mechanisms to message people about a page but they are not email nor a private communication. For your client it will be an issue. The only question is if they get enough FB complaints to suspend their account or if it only hurts their reputation.