If i remember corectly with Dijkstra's, you let it search all all possible nodes untill it find the node you are looking for, all A* does is adds an estimation to that cost to direct the search in 1 direction.
When running a Dijkstra's algorithm, you expend all nods equaly untill you find desired destination, so as long as you emmit the destination and let it search all nodes with a cost value less then max, it will work without any problems