You can set the lang attribute in your <html> tag if you want to. The w3c recommends setting it.
If you do set it, you the value should just be en, not en_US. It is a language identifier, not a locale identifier. It should only specify the language, and not the language and country.
However, setting the lang doesn't actually do anything. That ...
It can be fine for SEO to redirect the base URL of the domain to a language based on the Accept-Language header. The only SEO concerns are:
Test your rules for case in which the language header doesn't list one of the languages you support.
Test your rules for no Accept-Language header sent at all. (Most bots won't send one).
You need a fall-back page ...