Yes the alarm is a separate unit.
It's not that hard to access as well. You need to remove our wipers, then remove the plastic piece under that, the cowling or whatever they call it, a few bolts to remove, connectors etc.. And you are good to go... The alarm is located under there.. Looks like a hockey puck. I changed mine last year as mine was also causing he grief.. I'm not sure if just disconecting it would work as there may be info feedback back to the controller telling it that someone has disarmed the alarm... I'm sure you could find a thread here on the site with further info on this..