Yes, it works in Multisite, you could even activate it Network-wide. However, it does add almost nothing additional to the Network Admin but rather to the Dashboard of each individual sub-site of the Network. Therefore I recommend to use “Toolbar Extras” only in single installs (default) currently.
For Multisite installs I currently recommend my own plugin “Multisite Toolbar Additions” which is like a “sister plugin” of Toolbar Extras (and even was there before it!).
A special Multiste Add-On for Toolbar Extras is planned but no features or date is being set yet.