He uses women not just for a connection (and I mean both physical and psychological), but to inhabit their spaces, because at his very core, he is nothing.

Mad Men is an existentialist drama. These passages are long, but they explain it much better than I possibly could.

From the Wikipedia entry for Jean-Paul Sartre's Being and Nothingness:

Sartre contends that human existence is a conundrum whereby each of us exists, for as long as we live, within an overall condition of nothingness (no thing-ness)—that ultimately allows for free consciousness. But simultaneously, within our being (in the physical world), we are constrained to make continuous, conscious choices. It is this dichotomy that causes anguish, because choice (subjectivity) represents a limit on freedom within an otherwise unbridled range of thoughts. Subsequently, humans seek to flee our anguish through action-oriented constructs such as escapes, visualizations, or visions (such as dreams) designed to lead us toward some meaningful end, such as necessity, destiny, determinism (God), etc. Thus, in living our lives, we often become unconscious actors—Bourgeois, Feminist, Worker, Party Member, Frenchman, Canadian or American—each doing as we must to fulfill our chosen characters' destinies. However, Sartre contends our conscious choices (leading to often unconscious actions) run counter to our intellectual freedom. Yet we are bound to the conditioned and physical world—in which some form of action is always required. This leads to failed dreams of completion, as Sartre described them, because inevitably we are unable to bridge the void between the purity and spontaneity of thought and all-too constraining action; between the being and the nothingness that inherently coincide in our self. Sartre's recipe for fulfillment is to escape all quests by completing them. This is accomplished by rigorously forcing order onto nothingness, employing the "spirit (or consciousness of mind) of seriousness" and describing the failure to do so in terms such as "bad faith" and "false consciousness". Though Sartre's conclusion seems to be that being diminishes before nothingness since consciousness is probably based more on spontaneity than on stable seriousness, he contends that any person of a serious nature is obliged to continuous struggle between: a) the conscious desire for peaceful self-fulfillment through physical actions and social roles—as if living within a portrait that one actively paints of oneself. and b) the more pure and raging spontaneity of no thing consciousness, of being instantaneously free to overturn one's roles, pull up stakes, and strike out on new paths.

...

Sartre states that many relationships are created by people's attraction not to another person, but rather how that person makes them feel about themselves by how they look at them. This is a state of emotional alienation whereby a person avoids experiencing their subjectivity by identifying themselves with "the look" of the other. The consequence is conflict. In order to maintain the person's own being, the person must control the other, but must also control the freedom of the other "as freedom". These relationships are a profound manifestation of "bad faith" as the for-itself is replaced with the other's freedom. The purpose of either participant is not to exist, but to maintain the other participant's looking at them. This system is often mistakenly called "love", but it is, in fact, nothing more than emotional alienation and denial of freedom through conflict with the other. Sartre believes that it is often created as a means of making the unbearable anguish of a person's relationship to their "facticity" (all of the concrete details against the background of which human freedom exists and is limited, such as birthplace and time) bearable. At its extreme, the alienation can become so intense that due to the guilt of being so radically enslaved by "the look" and therefore radically missing their own freedoms, the participants can experience masochistic and sadistic attitudes. This happens when the participants cause pain to each other, in attempting to prove their control over the other's look, which they cannot escape because they believe themselves to be so enslaved to the look that experiencing their own subjectivity would be equally unbearable.