When you receive the Equity Release payout it will be capital for Pension Credit purposes. If your total capital - the Equity Release plus any other savings you have - is less than £10,000 it does not affect your Pension Credit entitlement, & you can spend it as you wish - to pay off the debt or anything else.
If your total capital becomes more than £10,000 when you get the Equity Release then it would reduce the amount of your Pension Credit by £1 per week for each £500 (or part of £500) that your total capital exceeds £10,000. If you then use the money to pay the debt it may be accepted as reasonable expenditure by the Pension Service. If they do not accept that, then they will continue with the reduced payments - i.e. treating you as if you still had the capital.
For a definite answer you need to contact your local CAB, or else ring the Pension Service. In any case, you need to notify them when you receive the money.