Yes you will reach the limit. Whether the containers are running or not is irrelevant. Additionally there are restrictions on how many you can create per hour.
Unless the API is for a very limited use case I don't think dynamically creating ACIs to handle workloads is going to scale well. It is expensive in terms of resources and price. Without knowing anything else about your system it seems like Azure Functions that can be triggered and do their work would be more scaleable. If you really, really need an isolated environment and containers are the only way to go then I think you'd have to implement some sort of container pool where you reused existing containers. This would reduce the resource cost, would be faster than starting up a new container (I would think) and allows you to better manage the API container usage. But this is completely dependent upon what your API is trying to solve.