Hey Bill,
With out of the box reports, you cannot report against more than a single Global Collection.
This would cause probable performance issues in most customer setups due to volume of data.
You should be able to do this with an Ad-Hoc report, because you can select multiple GCs there as well as an alarm filter.
I am certain you can do it in Jasper as well, though I know you aren't running it due to lack of multi-tenacy but figured I would let you know for future reference.
So the answer is yes, but within Ad-Hoc reporting - not out of the box reports.
Thanks!
Matt