Your sister is fortunate to have you supporting her through this very difficult time.
I had a diagnosis of bladder cancer 10 yrs ago, had a major resection of the bladder to remove it (as it had already infiltrated the muscle wall - I was 32yrs old) and 6 months of chemo - and was diagnosed with ms some 18 months later.
Since then, I have had many anaesthetics - some for minor procedures, a couple for bigger ops, and I cannot say that for me there was any direct correlation between ms relapses or exacerbations and any of the ops.
Having said that, it is important that her neuro is aware of what is happening and can give her whatever support she may need - the diagnosis itself and the anxiety and stress that goes with it may contribute to a (?temporary) worsening of her symptoms in any case.
One worry would be post-op infection as many here have had experience of the link between getting an infection and having a relapse.
Also, you don't mention what stage they think her cancer is at, but if she needs chemo, discuss with the neuro as well as the oncologist - chemo is immuno-suppressive, which can be beneficial to ms!
Last piece of 'opinion' - please get her to see a medical and/or radiation oncologist asap (if she has so far only seen a gynae) - just to be sure she is having the correct follow-up treatment - in my country, sometimes surgeons think they have removed all the cancer (and they most likely have), but to be safe and careful, an oncologist should be involved as they are the only docs qualified to decide on any follow-up treatment post-surgery.
Also, radiation or chemo is sometimes used prior to surgery...
I hope I am not being an alarmist, I just want your sister to get the best holistic care possible, and for cancer, this means onco and surgeon (gynae) working together.
It is a scary time, but with you and a great medical team working with her, she will get the best treatment possible.
I agree with Gwa - the cancer is the immediate threat, ms is more chronic and any further relapses can be dealt with IF they happen - the main thing is to get her through this new and horribly difficult challenge.
I wish your sister all the best (and you too!).