I've been told both in NFHS and ASA not to do the equipment checks in the dugout - for a variety of reasons. I've never had the situation in the OP presented to me though. I suspect that if they were organized as described and the players were not in there too, I'd have checked them as is --- and then later asked my assignor for a recommendation.
And if someone I assign had asked me a similar question, I'd be asking a level up before responding.
Good question! I'm going to ask a level up now.