Even if you immediately state "inadvertent whistle", the ball is now dead, and either team can request, and be granted a timeout during a dead ball. Inadvertent whistle doesn't cover up the error.
Timeout requests are one of those situations where "metric" rules are a little better than the NFHS rules.
Now let me tell you about real inadvertent whistles, A1 fouling A2 during a rebound situation. Believe it, or not, this has happened twice to me in twenty-nine years.