yes, most married men can become priest in the orthodox church. there are rules regarding the marriages of those who would be ordained. for example it must be a first marriage for the couple. if the husband or the wife have a previous marriage the husband cannot be ordained. there is quite the list of canon law that must be met before ordination.
beagledave, some of the rules are the same betwix orthodox and catholic. one of them is the deacon thing. ordination must follow marriage. marriage can not follow ordination, unless the ordained steps down from that position.
i do know of a bishop in the orthodox church who waited until he was in his 50’s before he was ordained a priest. he said he kept hoping for a wife first. i guess he finally gave up and figured having a wife and family wasn’t in the plans. i also knew a priest that after his wife died he entered a monestary and ended up as an archbishop. it was a bit strange seeing kidlets running up to him yelling: “grandpa!”
having a family and a parrish does create problems for a priest. you and your family are held up to a rather impossible standard. sometimes a priest will have to wrestle with the question: “does he save his marriage or his ordination?” but if the rules were changed to make life easier we would be eating meat on fridays.