Possibly. e.g. We have just been married by a kind priest. In this context, the priest "marries" the couple (a secondary use of the verb "to marry") More commonly, the word "married" is used as an adjective e.g. My wife and I have been married for 2 years.

If the conversation goes something like this - Are you married? Yes, I am. I've been married for 15 years. - the answer is No. It isn't a passive. 'Married' is an adjective - the opposite of single. The construction is no different from saying this: Are you ill? Yes, I am. I've been ill for a few days. In both these cases, we're simply using an ordinary adjective with the verb 'to be'. The form 'have been' is the present perfect of 'to be'. As Michael has pointed out, there are a few occasions when [ to be] + married can be a passive form. This is when we are using the verb 'marry' in its more unusual transitive sense of 'to perform a marriage ceremony'. So you might say: 'Do you know Father James? He's the priest of our local village church.' 'Yes, we were married by him last year'. This means that the priest performed our marriage ceremony. As you can imagine, this is not a very common kind of conversation. 99% of the time, when we use the word 'married', it is an adjective, not a verb form.

Yes, it's passive.