No, because 있는 (있다 -> to have (in this case)) acts as a participle (verb acting as an adjective) in this sentence. This happens because adding ~은/는 to a verb makes it an adjective.
So 남자는 아이가 있다 -> Man has a child. 아이가 있는 남자 -> Man that has/possesses/is with a child.
That would be 아이는 남자하고 있어요 (or whichever politeness level of 있다). The example above is not a sentence, but a noun phrase consisting of a preposed clause modifying a head noun.
I wrote "a man with children" and it says I'm wrong. I guess I'll only count it as plural if there's -들- in it