If it is this type of 9V battery
it might work but not very long
let's estimate your servo is pulling 200 mA
The capacity of such a 9V-Block is 500 mAh
This means this battery is empty after 2,5 h of operation.
500 mAh / 200 mA = 2,5 h
If you want to run the real thing the servomotor will pull more than 200 mA
There is another problem with these 9V-block batteries
The inner resistance is medium high.
This means if you pull a current of 500 mA from this battery the voltage will significantly drop down through the inner resistance
For measuring all this a digital multimeter is very useful.
You can go on tinkering without a digital multimeter but you will have various situations where - without a digital multimeter you will scratch your head asking "what is wrong?" and then doing a lot of improvised stuff to analyse it
While with using a digital multimeter would make the analysing 2 minutes short
best regards Stefan