anal fistulas are not usually surgically removed, they are drained by placing a drain in place, the patient is given anti biotics to get rid of the infection, once cleared they usually heal themselves. The Ovarian cyst will not interfer with this procedure at all. Except one is called a dirty surgery, the anal fistula, and the other is a clean one. If the surgeon is very carefull about cross contamination the drain could be placed while under the anesthetic for the cyst removal. Good Luck make sure your surgeon talks to you about what he/she plans to do.
I do not know if the surgeries can be done at the same time, that is a question for her doctor and without knowing the type of surgery your mother is having to remove the cyst or will they be taking her ovary and tube? Is it being done laproscopically? Her age can also make a difference in recovery.