Your radar is your advantage, which you do no give up lightly. The most they could know is that there is somebody they don't like around here somewhere, but you know exactly where they are. Who is better off?
Now if you turn off your radar, the advantage is exactly even. Through most of the war there is no Japanese radar detection whatever. I'm in late September 1944 and still have not seen evidence of ships or planes homing in on my radar. I use it 100% of the time.
Real life example, CDR "Hobo Joe" Enright of the Archerfish when stalking the Shinano, left his radar on in spite of the near certainty of detection. In fact, the radar was central to the bad decisions made by the Japanese captain, resulting in the final jig toward the Archerfish which resulted in six hits by the American torpedoes.
This is war. Your mission is to attack, not dive deep and put your head in the sand. Stay on the surface whenever possible, with radar on to extend your search area to the maximum number of square miles. If the enemy detects you and comes to you they have spared you the effort of going to them.
If you must dive stay at periscope depth as long as possible. Retain the initiative. Attack. Kill. Live.
