Yes, it helps if you can speak in public. You can speak at tradeshows, conferences, seminars, meetings, teleseminars and so on. You can teach courses and get up in front of people all the time.
But, no, you don’t have to be great at public speaking. You can manage clients via direct mail, email, phone calls, one-on-one meetings, conversations and so on. Introverts have tons of great business qualities.
The key is to build on your strengths and to find ways to mitigate your weaknesses. Try doing a personal inventory to figure out your best qualities and where you need more practice. Focus on success and you’ll find a path.