Yes, if you have a contact that is still too far away to follow visually, you will need to submerge and follow it with the hydrophone.
I would suggest going deeper than periscope depth. Probably 25-30 m at least for your hydrophone checks. And especially if you're going to be running submerged for any length of time with no contacts at all in visual range. I don't know how closely it holds true in the stock game but in general, deeper = safer. Provided you don't go below crush depth, lol.
There's just no reason to stay at periscope depth if there's nothing close enough for you to see with the 'scope anyway. And if you're submerged, you will probably pick up any contacts with the hydrophone long before they get close enough to be seen. You'll have plenty of time to get back to periscope depth (or the surface) when you start getting near enough to make visual contact with the 'scope or from the bridge.
But always do a periscope check before surfacing completely! Even if your soundman reports no contacts. Just a good habit to get into IMO.
