The soulution exists, though it's quite complicated, and I'm not sure it'll suite you.
First, you need to create two Groups:
- 1-st will contain all your colleagues (only real people) (let's name it WithoutTicketSystem)
- 2-nd will contain all your colleagues + your ticket system (let's name it WithTicketSystem)
Second, you'll have to create two separate calendars for these two groups. They'll be almost identical with the exception of your "ticket system" user. The first one won't contain it, the second will.
Third, you'll need to configure your source so all the messages by default are sent to "WithTicketSystem" group (as a result, ticket is created) and the ones with "Server is Up" in the subject (as an example, it depends on the messages format your alerting system is generating) are sent to "WithoutTicketSystem" group (as a result ticket won't be reported, but all the same users will be informed)