The words groovy and rad seem to be used by people in certain cultures but are almost unambiguously good things. I don't think I've ever heard them used sarcastically. People might say "well that's cool" to mean that it's not cool. Some people say "have a nice day" to mean F you.
I have heard alternate uses for groovy. It can be a synonym for granola (the adjective, not the noun). If you can recall a time you heard either groovy or rad used in a bad way, please let me know in the comments.
This post partially inspired by Millencolin's song "Fox."