I think you misunderstand the use of en in these cases. It doesn’t change the meaning, it doesn’t turn something real into some fantasy.

For your pizza example, in both cases you are saying that you have cavities just by thinking about eating a so sweet pizza. Of course it’s not true.

It’s exactly the same thing with the second example, with the little difference that you say you have chills, which can be true (you can have chills just by thinking about something cold, but however you can’t get sick (still you could say “je tombe malade rien qu’à l’idée de…”)).

So I’d say the use of en has the only purpose to emphasize.

“En” is a pronoun that replaces the initial sentence. Note that in “J’en ai des caries rien qu’à y penser”, en is not necessary since y (another pronoun) has the very same role. Your second exemple is incorrect French. The en, being a pronoun, must be recalling something, and that something cannot be after the pronoun. That sentence would work just was well without it.

A better exemple where en changes the meaning:

• Je regarde la mer, j’en ai des frissons
• Je regarde la mer, j’ai des frissons

In the first sentence, it is clear that the shivering is emotional, while in the second, the shivering may be unrelated (for instance, due to cold wind on the beach)