Yes, certainly.
The regular set of documents of Your Seychelles IBC (if properly certified by notary and legalised by apostille) corresponds to the formal requirements of most banks, as far as the internal structure and configuration of the company itself is concerned. However, as described above, in order to open a bank account for an offshore company, the most important matter is the background and the proposed business details of the actual owners and controllers of the company.
Many beneficial owners would operate their offshore companies in a fiercely independent fashion and would open their offshore bank accounts independently, with bankers that they may already know. This is a perfectly acceptable.