Does anyone know if a creature (such as an Incubus) with telepathy would automatically know if someone was within 60 feet of him through the telepathy? For instance, an invisible creature.

Thanks for your input.

The spell (since there aren't details in the monster power, I go to the spell for a description) reads you can target a creature you know on the same plane (or, actually, for an incubus, if its charmed it can be on another plane). I think the relevant part would be if it knows the target creature. If the incubus knows the target, he can establish the link, even if the target is invisible. If not, say, its never seen the invisible creature before, then they could not establish the link.

I don't read telepathy as radar for mental activity, more like a way to make a phone call to a specific person.

No.

But it doesn't require sight either.

It's not much different than using a voice except you have to choose who can hear you. Being able to speak doesn't automatically let you know if somebody is nearby able to hear you. But if you knew there was somebody hiding in the closet you could go to that closet and talk, even whisper, to them without seeing them.

If the Incubus/Succubus knows you are there, they can speak telepathically to you, but won't know where you are if they cannot see you. If they don't know you are there then they cannot speak telepathically to you.

EDIT: Xalthu posted while I was typing and so I will add: the telepathy used by monsters as a language is not the same as the spell of the same name.

Monster Telepathy, when given as a language, follows the rules given in the Monster Manual:

Telepathy

Telepathy is a magical ability that allows a monster to communicate mentally with another creature within a specified range. The contacted creature doesn’t need to share a language with the monster to communicate in this way with it, but it must be able to understand at least one language. A creature without telepathy can receive and respond to telepathic messages but can’t initiate or terminate a telepathic conversation.

A telepathic monster doesn’t need to see a contacted creature and can end the telepathic contact at any time. The contact is broken as soon as the two creatures are no longer within range of each other or if the telepathic monster contacts a different creature within range. A telepathic monster can initiate or terminate a telepathic conversation without using an action, but while the monster is incapacitated, it can’t initiate telepathic contact, and any current contact is terminated.

A creature within the area of an antimagic field or in any other location where magic doesn’t function can’t send or receive telepathic messages.

Telepathy is not the ability to detect thoughts.   It requires each party to intend to send thoughts.

Unless their ability expressly says " ...learn the surface thoughts of the creature...", they do not know if someone was within 60 ft.