Almost always — but not universally. Some tools use comments as directives: Oracle optimiser hints (/*+ INDEX(...) */), MySQL version-gated comments (/*!40101 ... */) and query-tagging comments used by APM tools all live in comments. If your query uses any of those, turn comment stripping off.
Does the minifier understand quoted strings?
Yes, and this is the main reason to use it rather than a find-and-replace. The minifier tracks single quotes, double quotes, backticks and T-SQL brackets character by character, so a literal like 'a -- b' is preserved intact instead of being truncated at what looks like a comment marker.