Yes, absolutely.
The standard set of documentation of Your BVI Business Company (if properly certified by notary and legalised by apostille) will correspond to the formal requirements of most banks, as far as the internal structure and set-up of the company itself is concerned. However, as indicated above, in order to open a bank account for an offshore company, the most important aspect is that of the actual owners and controllers of the company, their background and their proposed business details.
Many beneficial owners would operate their offshore companies closely by themselves and would open their bank accounts independently, with bankers that they may already be familiar with. Going this way is perfectly acceptable.