Evidence suggests that Charles Whitman's brain tumor was pressing on a part of his brain that could impact his emotions and actions, but there is also a wealth of evidence that points to the fact that Whitman was troubled long before both the brain tumor and the shooting. He had a difficult childhood, had been discharged from the military for gambling and possessing a firearm. It's not unfounded to believe he was inclined to violence.
No, Charles Whitman would not have murdered those people of his tumor had been removed. Following the shooting, a task force commissioned by Texas Governor John Connally, composed of neurosurgeons, psychiatrists, and pathologists, concluded that Charles Whitman had a brain tumor, which could have contributed to his inability to control his actions. In the year leading up to the shooting, Whitman had visited several doctors for help with his violent impulses. If those doctors had discovered Whitman's brain tumor, the massacre could have been prevented.
Looking at this at a more technical way, I don't think Whitman would have killed those people because he would have been spending his time recovering from a brain surgery that was a lot more risky back then. He would have died or spent his time in recover, which would ultimately change some paths in his life. As for the affect the tumor had on him, I don't think it was the only thing that pushed him to murder so I wouldn't solely decide my decision based on it's effects.
As someone who enjoys learning about the inner workings of the mind and the reasoning behind why people do the things they do I find this question very interesting. It's hard to say that as a trained Marine and man who felt he couldn't communicate his feelings with his family and friends, if the tumor had been removed the terrible happenings of that fateful day wouldn't have happened. While there is no doubt that the tumor negatively affected his thinking which led up to his emotional state that day. But can we place total and complete blame on the tumor. He easily could have been suffering from PTSD or other equally debilitating issue. However the rapid onset of his symptoms and the change in his thinking would lead one to believe that it was the fault of the tumor. Unfortunately, I believe without actually being able to talk to Mr. Whitman himself we can't know for sure.