If you are speaking of an offshore account it is a little more complicated than that -- funding is not a means of proving anything as funds can come from clients or even in some cases digital currency exchangers depending on the banks. Some banks do require you fund from a current personal account to confirm identity but those are usually UK/EU banks and not true offshore banks.
Most offshore banks will require the following:
1. Notarized passport or government ID
2. Proof of address such as a bank statement or utility bill
3. 75% of the banks also want a professional reference letter from a banker, lawyer or accoutant
No real offshore bank allows for online only account activation -- although some allow you to create the account pending your identity documents.