If I count as an American for the purposes of this question despite not growing up in the USA, I'd say yes. I was raised to say "darn" or "dang" or "heck" instead of "damn" and "hell", and I'm still caught a bit off guard when I see these words used in things like anime subtitles because I'm still used to thinking of these as naughty no-no words that you're not supposed to say on television — at one point as a kid I didn't even like talking about dams, but the grown-ups around me assured me that it was OK to say "dam" in that situation. I think that might be part of why I generally prefer to say "damned" instead of just "damn". I also generally capitalize "Hell" even though others don't, just because Hell is supposed to be a specific location.

Though curse words do come in tiers or gradations, and "damn" and "hell" to me have always been in a lower tier of vulgarity than "fuck" and "shit" and "oge 'e boo".