Anyone with a Jewish mother is considered a Jew and can choose to life the religion to that extent. However i am quite sure you will need to have made the decision and devoted your time to the necessary studies years before military service for the exemption to be granted.
Think of it this way. Any christian can decide to move to a monastery as a priest or nun. But if he wants to do that not to get drafted he should do that a bit earlier than the draft date.