It depends on a lot of stuff.
In real life, periscopes can be detected by radar, but it's not easy. Basically, unless you leave your mast up for an absurd period of time in calm weather, you're not likely to be detected. Some radars are better than others, though. There's several radars out there designed to specifically spot periscope masts because ordinary surface search radars don't always catch them. Those are really good at picking out periscopes, and are actually pretty interesting. Maritime patrol aircraft usually have a radar that's really good at detecting periscopes. Surface ships typically don't.
Currently, though a periscope is more likely to get spotted by a good lookout on top of the pilot house.
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