[thaumasiotes]

There are good reasons to think of it as being a word. For example, much like the particle 's, it applies to a phrase without being at all concerned with what word it modifies. (Think "a week and a half ago"; which word would you argue "ago" is being suffixed to?)

Does this make it different in any meaningful way from an agglutinative morpheme? No, obviously not. Whether to call a language "agglutinative" is already more a question of cosmetics than facts. It reminds me of the feature tagging guidance on Universal Dependencies, which notes that no language can ever simultaneously have "gender" and "noun class" features, because they are the same thing. If there are three or fewer, the feature is called "gender"; if more, "noun class".

[onlyrealcuzzo]

It applies to week-and-a-half, which is a phrase only because there's not a word like fortnight means "two weeks"...

[thaumasiotes]

It applies to a phrase in all cases. If you don't like "a week and a half", you should rethink your approach to the problem, but you can still consider examples like "five years and fifteen days ago".