No.
The way it used to be, and this has changed, swabs were divided into three companies during Swab Summer, X-ray, Yankee, and Zulu (X,Y, and Z). Within those companies the swabs were broken into platoons (1 through 3) and within those platoons swabs were broken into squads (1 through 3 and a training squad). In the last week of Swab Summer swabs were notified of their 4/c year company assignments. After 4/c year you were given your "real" company assignments. Some companies focused on specific things, like the color guard or flags, so a 4/c could request to be assigned to that company (had to be for a good reason, and even with a good reason it didn't mean it would be done).
Example, I was in Yankee Company as a swab, Y-1, squad 1 to be exact. After that I was assigned to Charlie Co. After a "no-so-fun" year with the Charlie Co. Cobras I was assiged to Bravo Co. It is in that final assignment that you will grow closest with those Company mates.
Now, as I understand it, some of that has changed. What I'm going to say now is from what I heard described from a 3/c assigned to my cutter earlier this summer. It had been discussed in the past, and actually makes sense.
I believe now the Swab Summer battalion is divided into eight companies, Alfa-Hotel. The cadre of each of these companies are actually in those companies, and the swabs in each company will be headed to those companies their 4/c year. As I remember it, the change was meant to correct a poor example be set by cadre. During the summer they were "hard-core" but many changed during the school year and seriously slacked off. It was thought that this might "keep them honest" because they knew their swabs would be watching them, and learning from them, and therefore they needed to set a good example. I don't know if that thought became reality. I believe they still switch companies after that first year though, giving them a fresh start and allowing them to creating a working relationship with the class above and below them.