I’ve worked in this space and written software that communicates constituent opinions to Congress.
At the congressional level they don’t take emails seriously at all, or pay much attention to them. They’re triaged using constituent management software into email lists with auto-responses for different issues. Actually Congress has an API that approved software vendors use to send constituent opinions and group them by associates issue or bill. Congress members no longer publish their emails and have contact forms on their website instead, that feed into this API along with other vendors (ex: countable.us)
At the local level it’s a different story. Some use software to organize the emails, some actually monitor and respond to emails, it depends.