Hi Anne
by coincidence we have just today been working on improvements to this which includes a bug fix that won't yet exist in your installation but for which there is a temporary workaround you could use.
Firstly to answer your question yes the screen reader software will read the 'Tooltip Hotspot' you give to each hotspot. The improvement we have been adding is an optional property for each hotspot where you can add longer 'All text' descriptions for each hotspot that will be used instead of the short label if added. That will be part of a future update/release.
The bug we found was with the tab order on the hotspot connector page whereby if a user tabbed to the hotspots the first hotspot in the tree wasn't being picked up. We have fixed this but you will need to use a workaround until the update can be applied to your installation. Simply add a tiny hotspot (perhaps bottom right corner) and keep that at the top of the tree. When a user tabs around that hotspot will not be picked up and when your install is updated in future you can just deleted that temporary hotspot.
I would also install NVDA
www.nvaccess.org
so that you can test this kind of thing yourself.
HTH
Ron