Honeywell makes a lot of different devices using a lot of different protocols, so we would need to know the exact model, but my guess is not.
Also, I’m concerned if you think you’re going to beat a three second response time. Most of the inexpensive home automation sensors that are battery-operated are “sleepy devices” which literally sleep most of the time in order to preserve battery life. Then they wake up periodically and check to see what’s going on. Quite a few of the motion sensors are set for 5 second periods, which means they may not detect motion for the first 5 seconds. That’s OK for intrusion alerts inside the home, but it means they might very well miss the period You are trying to catch. You can dial the sensitivity up in some cases, but then you had the same issue you’re having with Arlo, you’ll run to the batteries much faster.
To get much quicker response times, you typically have to go to wired sensors, which don’t have the power preserving issue. But that may not suit your use case since you have to run powerlines to them.