If my noob experience is anything to go by, yes. At least in the stock game, night surface attacks seemed a sure way for me to explore the absolute bottom of the seabed, one time only. In moonlight, early detection even before I spotted the enemy ships seemed assured. I gave up trying to make night surface attacks for that very reason, and certainly started to treat moonlight like it was high noon.
Ducimus says that TMO2 is supposed to change the parameters on that score and make visual detection a bit more realistic, but I haven't had the chance to try it out yet.
IIRC, there is another thread on here about moon phases and star positions etc. I can't recall where it is or what it said, but a quick search may find something relevant. There might even be an online almanac somewhere you could refer to at the start of a patrol. Failing that, take up amateur astronomy and back-time the phases for yourself. Then let the rest of us know what you come up with!
On the reality front, from what I've read, skippers would avoid surface attacks under moonlight and would sometimes specifically hold off on action (torpedo attack or shore bombardment) until the moon had set for exactly the reasons you mentioned.
Another question I've had is if the game is sensitive to phosphorescense. Fluckey writes that it was part of the OOD brief to him anytime something was sighted at night, to alert him to tactical conditions on the surface.