In Stock, no. SD is always on, unless you are underwater below RD (PD with mods), and if you have SJ, it turns on automatically when you surface - but there is a reason for that... waves...
In FotRSU, instead of an up / down for the SD, we use On / Off, so that you can approach any place, but especially home, and not be interrupted with "Radar contact..." That also helps if you are trying to "stealth" your way somewhere after dark. The SJ still turns on automatically when surfacing or at RD, but the reason being you do want it to come back on if a wave washes over it. But you can turn it of separately from the SD.
No matter the mod set, or Stock, always consult your SH4_Q-Ref_Card_Back.jpg and SH4_Q-Ref_Card_Front.jpg images in the game's root folder for the key combinations for both (and other stuff, of course).
