One of the first MSQ quests will stop you from continue if your gear isn't good, so it will be not a surprise if we can get this check on any dungeon.

But, one important thing is, the check must be performed when:
- you queue a duty/roulette (all duties with IL>your one will be excluded from roulette [will be funny have people lamenting they only go sastasha...])
- you confirm participation (cannot confirm if gear doesn't pass)
- into the duty itself (cannot trollchange your weapon/gear/accessories when into the duty)

And all the above NOT apply when you go undersized/premade.