Also; if you're NOT talking about an actual PRESET (like one you edited and custom made NOT using the default markings, because some people do call their characters presets even if they're not), then yes, in a private map your character will be visible, same as any other map. If it's a true preset with custom markings or whatever then they'll just see the white, textureless character that people see when they don't have preset files.
Preset: custom character made using the "preset maker" ingame.
Character: custom character made using the "character creator" ingame; this is what most people use; made with default markings.