Somewhat. The "Staff of Magus" spell does draw directly on the staff's own stats and you may find it worth using in certain circumstances, and perhaps often if your staff has a high chance to proc one or more nasty status effects.

Yes, the one thing that improves with a high Damage staff is the Staff of Magus spell. Interestingly even if you your are too lowlevel for the staff you pay the same amount of AP for the Staff of Magus spell.

Sadly, that Staff of Magus spell seems hopeless underpowered to be of much use. I used it twice in the beginning when I had a special resistance that I couldn't counter with the right spells yet.