I think it's inappropriate to hound enlisted soldiers who don't share your particular brand of faith, yes. Chaplains serve their own communities of faith within the services. It's not appropriate to go lower morale among others by telling them they're wrong and need to get right with you. That's not what they signed up for.
"hound"?
Your language betrays you. Chaplains should invite military personnel to their services; this is proselytizing and there's nothing wrong with it. As a Christian, the Chaplain might then have a sermon at that service in which they quote Jesus, "None come to the Father but through me." Then they should answer any questions that come up. Spritual pressure? You bet.