Yes, the books are related and are intended to be read in order. In Search of Lost Time is one work in seven volumes. Each volume is not an independent work. Rather, the novel is a developing story; the narrator is relating events from his life, and each volume furthers the narrative. Outside of specialized research or publication/translation contexts, it is rare to find the individual volumes being treated singly. The English Wikipedia, for example, does not even have separate entries for each volume. (The French one, however, does.)
It is true that some sections of the narrative are relatively self-contained. For example, Roger Shattuck points out:
The first two sections of Proust's novel, "Combray" and "Swann in Love," can stand separately and have earned many admirers.
Similarly, the second half of Sodom and Gomorrah (volume 4), and the entirety of The Prisoner and The Fugitive (volumes 5 and 6), constitute what is called "the Albertine cycle". Aaron Matz says of this cycle:
Despite all their connections to the earlier volumes of the novel, The Prisoner and The Fugitive (along with the second half of Sodom and Gomorrah) constitute a novel unto themselves, a total fiction.
However, from both Shattuck's and Matz's articles, it is clear that these relatively self-contained narratives don't map cleanly to individual volumes. In talking about the "first two sections of Proust's novel", Shattuck means the first two parts of volume 1, Swann's Way, which are thereby the first two sections of the novel as a whole; he does not mean (as one might assume) the first two volumes of the seven that constitute the entire work. And Matz likewise refers to the Albertine cycle as comprising half of one volume, and the two next volumes.
So a given volume of Proust's work does not itself constitute a self-contained whole. Characters recur from one volume to the next, and for the most part, knowledge of what went on in a previous volume is assumed in subsequent volumes.
Since Proust did not complete the final revisions on the last three volumes, some overlaps, repetitions, and inconsistencies occur, so the narrative isn't developed entirely in a clean arc. Proust's technique, too, isn't strictly linear. However, this makes reading the novel in order more important, not less; reading the volumes out of order will make the experience difficult and confusing (some might say "more difficult and confusing"), as you won't be able to tell whether some gap or inconsistency is due to the technique, the inadequate revision, or your having skipped a volume.