Aggravate, probably, but I would imagine there is an equally likely chance of developing tendonitis on any neck style depending on player's habits/technique/etc. etc.
I find a wide, thin neck more comfy than a skinny, boaty neck. Probably because of my long arms. My hands are only medium sized. Skinny necks (across the fretboard) put my hands in a more awkward position, and I would theorize an awkward position would cause more damage, i.e., CTS, than a comfortable position.
But, let's not overlook one major contributor to developing CTS: typing! Everybody stop typing and go play yer gee-tar!