Can forceful induced vomiting cause an aneurysm?

Not directly: but it can cause increased blood pressure or intra cranial pressure, which might pre-dispose you to a rupture of an aneurysm if you already have one. It can also cause bleeding and perforations of the esophagus, so forceful emesis is never a good idea.

No: Vomiting will not cause an aneurysm. It can cause bleed in the GI tract by tearing the inner lining, usually of the stomach where it meet the esophagus.