No, SEBI rules mandate that you are required to transfer the funds from bank accounts that are linked to your trading account. If you have transferred the funds from an unregistered bank account, you are required to submit the scanned copy of debit transaction statement with that make sure the statement has Account Name/ Account Number/ IFSC Code/ MICR Code/ Bank Branch. You can drop a mail to firstname.lastname@example.org.
Alternately, if you have transferred the funds from the unregistered bank, which is on your name then simply you can add the bank as a secondary bank, and the funds will be updated to your trading account.
Please Note: You can link up to 3 bank accounts to the trading account. One bank account will be the primary bank account, and the others will be marked as secondary bank accounts.