No, I don't believe you can do an aggregate function on the recordset object. If the recordset is using a client side static cursor the recordcount will be filled in, otherwise, on a read only recordset it will not.
If this is an Access database, it will probably be necessary to do a second sql call to get aggregations, such as the count. There are some manipulations possible on the recordset, such as, filtering and sorting, but aggregation is not one of them.