Key fob

Well, it isn't quite that bad. But if they did what they normally do when replacing a lost FOBIK one of the first things is to erase the lost units from the system. That way if someone had stolen it or just found it somewhere it is no longer a valid unit for your van. If it were attempted to be used it will trigger the theft system and immobilize the van and set off the alarm system if equipped. Now if you did find it you can go back to the dealer or an automotive locksmith, provide proof of ownership of the van and they can re-enter that FOBIK as a valid unit again but it wouldn't be usable until that was done. Even using the key section will trigger the system as it can read the transponder in the key even outside the van.

It may not have the optional contents alarm but it does have the immobilizer part of the system as standard equipment. That has been part of pretty much every vehicle made in the US since the mid 90's as well as most imports, and is something the insurance companies pushed for to reduce thefts. It will detect the improper key and prevent the engine from starting or running. That is why they warned you and had to program the FOBIK to work in your van. I have a 2014 Journey that is the same way. It has proximity entry, remote door locks and push button start, but no contents alarm.
Your Caravan and my Journey use basically the same electronics and adding the alarm is really nothing more than adding a dealer code for the option purchase into the programming, essentially just telling the vehicle, hey you have an alarm now, no other items added but a hood switch that plugs into a plug that is already there.