Your understanding is definitively good enough as a working hypothesis. The relation between alienation and unification is one of the major topics of the book, i.e. something not defined but explored. The Socienty of the Spectacle is much easier to read as a whole than as a system, i.e. repeatedly rather than incrementally. Still, let me provide some background and some explanation:
Alienation
For Hegel, alienation basically is the result of reflection: the subject presents itself as an object when we reflect on it; the same goes for all our parts and all we are part of, our properties, the categories we think in, society, nature. For Hegel the unity is generated by the spirit or (at least in Marxist understanding) by thinking: ultimately the spirit realises that all the things that seem to be other objects are really its own product. Now, Marx’ critique is this: Marx claims Hegel has got it the wrong way, that Hegel’s philosophy has to be put on its feet. To understand this, recall Hegel’s Philosophy of Right: Hegel starts with the notion of property, this notion then leads to contradictions which require the new notions of contract, law, moral, family, society, and, finally, the proper »State« in which all the contradictions find their solution. One part of Marx’ critique is that Hegel only presents the ideal of unification but not the real praxis (the economy) which actually unifies. Perhaps more importantly, he tries to inverse the process: What if, Marx asks, the totality is not the reconciliation of contradictions but rather the process by which the contradictions (property, or, for the later Marx: commodities) are generated in the first place? This question is the basis for Marx’ project. But this reversal has important consequences for the notion of alienation: alienation no longer means that we have not (yet) understood that we and the object we are regarding are really the same; rather, our totality produces real contradictions, it produces conditions in which our parts and what we are part of, our products and what we are produced by, are not »ours«.
Unification
While in Hegel, alienation and unification can be seen as opposites (the alienation ultimatly disappears only in the final unification), even for Marx this is not true: the capitalist mode of production unifies (almost) everything, but alienation remains: the products of the worker are not her own, but present themselves as an alien and potentially hostile power. In Marx, however, the unification is not total, because the remaning alienation (although the later Marx no longer uses that notion) is understood to be visible and the necesessity obvious to abolish dispose of the mode of production that creates said alienation. This is where some 20th century Marxists disagreed: It seemed that the unification indeed tended to become total, and the question became how to explain that.
Debord provided one of these attempts.
Society of the Spectacle
›Alienation‹ occurs for the first time in Thesis 8: this is pretty Hegelian, »reciprocal alienation« means that »reality« as well as »spectacle« become what they are not, reality because it presents itself in the spectacle (therefore as something else than reality), while the spectacle is real, e.g. a spectacular concept of reality. While for Hegel and Marx alienation was between subject and object, Debord describes alienation in a process that is already removed from the subject. According to Marx, the subject creates her own alienation by producing; not so with Debord: the alienation has already happend before the subject even appears.
In Hegel, contemplation of the object is the process by which alienation is ultimately overcome, For Marx, contemplation (or thinking) provides us with what is required to change the conditions that create alienation. But for Debord, contemplation is exactly that what creates alienation: when we contemplate (watch, observe) we do not really critically analyse. Rather we understand reality in categories provided for us, in categories we use but did not create.
For Debord these categories (the spectacle) structure and constitute what is real to us. They create our reality. And they combine every aspect of reality. Everything fits. That is unification. At the same time, the spectacle (the cultural discourse, the political discourse, the way we see our surroundings in our roles as workers, commuters, tourists, revellers, etc.) is somewhat removed from what we really do (as opposed to our role).
Unification means that everything fits together, everything can be explained by something else and, therefore, everything that is can be justified. If alienation can be justified, any hope is lost. Debord’s project hinges on the hinges on the possibility that the unification is a wrong one.
So while Debord tries to explain why alienation and unification must present themselves in our society as identical, his project requires that we still can distinguish between them. And, indeed, there has been much discussion, if and how this is possible.