The call should only run for under the minimum 100ms each time as it's just a ping and the instances is usually already loaded although AWS will likely recycle the instance from time to time outside of your control. There would be roughly 8640 calls/month which is about 864 seconds of execution time. You get 800,000 free seconds per month. This is totally negligible because even if you are counting it above the free level it is about 7/10 of a cent per month.
From my understanding of the pricing (I could be wrong), even if the call is 100ms, because the timeout is set to 300s so the app stays in cache, you'll be charged for 300s (app is "running" for that long).
Disclaimer: I am a Lambda fanboy.