My dad did something similar by accident on a family trip many years ago. We had a Scotch cooler (it's a round metal cooler with a tight fitting lid and a tartan pattern on it) and prior to heading home my dad put some peaches in it, and for some reason he had some dry ice so he put that in to cool it. This lid must have leaked just the right amount to hold some pressure, but not blow off. After we got home (8+ hr drive) we had fizzy peaches!
I would be very surprised if you don't get fizzy tomatoes.
Side note: the apples, pears and a couple other fruits that are stored for long periods (up to 9 mo. - apples in late spring, early summer) before going to market are often stored in a cooler with high CO2 levels. Not enough to cause fizziness, but enough to prevent the fruits from rotting.