If I've made Hangouts handle my SMS, is there any downside to disabling the default Messaging app?
Does anything rely on that app being enabled?
On some devices, especially Motorola ones, disabling the stock Messaging app will cause any app that you set to handle SMS to crash when sending an outbound SMS. While other system apps may be safe to disable, I would recommend against disabling the stock Messaging app.
See this question for more details.
I haven't experience any major problems after using the integrated SMS/Hangouts. Only thing is that you may take some time to get used to it. However, it's a matter of preference. Some may prefer separate apps to avoid pain of selecting whether to send SMS or start a Hangout. But to answer your question, no, nothing to be taken care of.