Does a negative accounting profit imply a negative or zero economic profit?

No, only if we keep the purchasing power one the monetary unit constant.

If the purchasing power of money is increasing (we have an fall of prices in general), we can have an negative accounting profit but an positive economic profit (Accounting profit - Interest - change in the purchasing power of money).

An example is that an company paid 100 dollars for the factors plus 10% interest that will be paid in the end of the period, in the final period the total cost will be 110, if the company had an receipt of 105 this can be saw as a loss, however when accounting for the true profit the company compares the current, or better saying immediate past and very short run future, prices with the receipt. So if the machinery and works and etc., are now costing 70 and even without adjusting the interest to expected fall in the future prices, he will now that his economic profit is 25 (70 for the prices of the factors plus 10 from the previous interest contract).

The economic profit is the liquid real income of the company at the end of the given time.

The opposite is true, positive accounting profits can be negative economic profits.