Can multiple sclerosis cause sciatica pains?

Yes. Its possible since MS can affect nerves not only in the brain but also in the spinal cord. Alternatively, diseases like Transverse Myelitis (related to MS) can occur and cause pain in a sciatic pattern as well.
Possibly. Ms is the great masquerader. It can present in a multitude of ways. It all depends on where the plaques are anatomically in the brain or spinal cord. But in medicine as in life common things are most common, so first it should be assumed that sciatica is due to herniated disc and MRI of spine should be ordered.
A bit uncommon. Greater than 90 % of MS patients do suffer pain, and leg pain is not rare. But always best to check that the sciatic like pain is NOT due to a ruptured disc in the lower back, or due to diabetes. Co-morbidities do exist in MS.
Can coexist. Sciatica is common so it can coexist with many other conditions without being etiologically connected.