No
There are 2 ways to recover an account
If you have access to the E-mail which is used to recover the account, you can simply request password reset.
You can click "No, I dont have access to the E-mail" on password reset page, that redirects you to the Recovery page, here you enter set of details which help you recover accounts. These details include Creation Date, Billing Information (If any), Country/ISP used to create account, current ISP, previous passwords, and additional Information which can help prove that you own the account. Jagex then reviews information submitted, and if the information is sufficient enough to prove that you own the account, they return the account back to you.