I was wondering the same thing. I think the answer is probably "yes, if your chat system can send you http when traffic happens". I think Lambda is probably a great choice, since each message in chat is an event to process according to the rules that your bot has. So, the Lambda function invocation model is a good fit - lots of tiny invokes. You might, though, want to filter the traffic that gets to the function, though, if your chat system is high-traffic.
For example Slack's Events API lets you subscribe to all of the things you might need the bot to see, I think. You'd then need to route those requests to your lambda function, which you could do via AWS API Gateway.
The existing hubot-slack adapter uses the Real-Time Messaging API, though, so you'd need to write your own adaptor for the Events API http that the API Gateway receives.
The same approach (and requirement) applies to other chat systems.