Physical: Yes. Incorporeal partners can be difficult to explain at family dinners.
Emotional: Preferably not. Or at least, if they are, able to restrain it and not liable to use it as leverage. Edit - passionate, yes, but emotional and/or sentimental - no thanks.
Mental: No, preferably not. I'm mental enough for both of us, and I need someone solid and relatively conservative to balance me out. I did say 'relatively'. edit - energetic. If I'm gonna spend a lotta time with someone they need to be pretty mentally energetic and agile. People who are too slow to catch on, or who nitpick and/or need everything spoonfed with examples etc, frustrate me.
Overall, must have a strong sense of propriety and etiquette. To teach me!