$or statement in $elemMatch

Sure it is, just clearing up the syntax but you basically had it:

{
    "opened": {
        "$elemMatch": {
            "closed": false,
            "$or": [
                {
                    "openingEvening": { "$lte": currentTime  },
                    "closingEvening": { "$gte": currentTime  }
                },
                {
                    "openingMorning": { "$lte": currentTime },
                    "closingMorning": { "$gte": currentTime  }
                }

            ]
        }
    }
}

And given a sample idea of the data:

{
    "_id" : ObjectId("537969cee90c3db84958aa86"),
    "opened" : [
            {
                    "closed" : false,
                    "openingEvening" : 17,
                    "closingEvening" : 22,
                    "openingMorning" : 11,
                    "closingMorning" : 14
            }
    ]
}
{
    "_id" : ObjectId("53796a47e90c3db84958aa87"),
    "opened" : [
            {
                    "closed" : false,
                    "openingMorning" : 13,
                    "closingMorning" : 14
            }
    ]
}

A current time of 12 would match the first but not the second document but a value of 13 would match both.

Also noting that these are within an array so given your estimated purpose you probably want a “dayOfWeek” field to include in there as well