Yes, you can set up a budget alert. I have it set up for one of my work accounts. Problem with that is that it's an email, and there's usually some delay in it going out. It's not a great solution for accidental traffic spikes (surprise HN post, or someone finding and abusing a public S3 object you have hosted, etc).

So you get an email saying your $10/mo site is now $1000 for this month, and climbing.

In general I wouldn't recommend using AWS and expecting the free tier for anything that's going to be public facing or autoscaling.