Simple answer, NO. Why? See below.
Most common ways Realtors get sued according to Inman.com:
1. Failing to disclose a property defect
2. Breach of Duty
3. Representing a client in unfamiliar territory
4. Giving legal advice
5. Misleading clients
6. Breach of contract
7. Failing to keep clients data safe
8. Failing to recommend inspections
10. Bodily Injury
E&O will cover most of the above claims, but will not cover you if you get sued for bodily injury or failing to keep your clients data safe.
For $500 or less I can write you a simple business owners policy that will cover you from cyber attacks, bodily injury claims, damage from open houses, and more. The best part is, if you get sued for one of these risks not covered by E&O, you won't have to hire an attorney because your policy will provide one to defend you. It's like having an attorney on retainer for less than $500 a year.
Give me call to discuss.