I don't think he's trying to use it as a pager tone, rather, he wants his pager to alert when it hears these attention tones. Perhaps, a buff, that knows when those alerts go out it's usually for the "good stuff" on the radio and not mundane traffic stops.
Either way, it does not matter.
The unsolvable problem is that console alert tones are totally dependent on how long the dispatcher chooses to leave his (or her) finger on the button. That basically disqualifies the tone as a possible way to trip the pager.
When I dispatched law enforcement, we used a couple of short beeps just to get the street's attention for minor announcements. A long press on the tone button was a way of clearing the air and letting the street know that a critical message would follow.
When we did fire and ems dispatch, the console alert tone followed regular paging tones, but was just a "heads up" thing with no fixed timing.
Any way you look at it, no fixed tone duration means it won't reliably trip a pager.