No, falling overhead cost per unit of output does not imply a situation of ever rising profits. Because-
(i) Overhead costs are fixed costs. These costs are constant, no matter what the level of output is. Accordingly, per unit fixed cost is bound to fall as output increases.
(ii) Fixed cost is only a component of total cost. The other component is variable cost.
(iii) While estimating profits, we must account for both the fixed costs as well as variable costs.
(iv) It is only when the difference between total receipts from the sale of output (on the one hand) and total cost of production (on the other hand) is maximum that total profits are maximised.