Yes. Smart Emails needs to stay installed for live changes to work.
Why?
After the initial export, Smart Emails pushes text, color, and setting changes to Shopify in real-time. If you uninstall the app, these live updates stop. Your exported email templates will still work, but they will be frozen in their last state.
What happens if I uninstall?
Your exported templates stay active in Shopify
Live changes (colors, text, translations) stop working
You can reinstall anytime to restore live changes