No. They are feeling their own state of consciousness, their own presence, not his. Yes, if you are spiritual, close to the realization, or an experienced meditator, being in a presence of an enlightened person might yank you into the “thoughtless state” and a feeling of peace and bliss. But it’s only because you allowed it. And you probably have to believe he’s enlightened, too.

Otherwise his presence will not be any different from what people call “presence” in everyday life. Many people can look you in the eye and listen attentively. You don’t have to be enlightened to be able to do it. What you could notice is your inability to invoke any emotion in him, to connect with him on a personal level, and it might seem somewhat uncomfortable, offputting even. But to do that you’d have to get into a conversation with him outside the context of enlightenment. If you’re emotional and judgy he might even seem cold, distant and closed off to you. Your ego is absolutely capable of making that interpretation as its protective mechanism. Or he may appear soothing if you suffer from your emotionality. In a word, how you will feel him completely depends on you, not on him.