Do Web Components work with IE11?
Short Answer: Yes, through a polyfill. Google created and maintains webcomponents/polyfills so it should work, but with porting features back to old browsers, your mileage may vary.
🙋♀️ Worth noting: IE11 support ended June 15th, 2022 (source)
TIP
Due to the progressive enhancement superpower ✨ nature of Web Components, you may be able to structure your site in a way to not need a polyfill. Depends on your situation, but un-enhanced LightDOM may be able to provide a suitable fallback.