I see now in the comments that the OP has now mentioned a specific, special guitar, and @leftaroundabout has answered with the appropriate information for that guitar. This is answer is applicable to most conventional electrics, but is probably not to relevant to the actual guitar in question.)
You don't have to take them off, but you should loosen the strings before adjusting the truss rod, particularly if you are tightening it to lower the action, which stretches and increases tension in the neck.
You can damage the neck or the truss rod if you don't, because of the tension from the strings pulling in the opposite direction, particularly if you are using high tension strings.
That could cause your truss rod adjustment to have less effect than otherwise, although on a guitar that seems unlikely, especially if you tightened almost a complete turn. (I surmise it would give out with some ugly noises when that was happening.)
You can also strip the truss rod nut by tightening it to too much (I did that once, although it was a 5 string bass with heavy strings and a 35 inch neck), or it might be a factory defect, as @b3ko has mentioned. See this article about that: Guitar Shop 101: Dealing with a Stripped Truss-Rod Nut.
Regardless of the article, I am with @SkinnyPeacock - you've got a good guitar and you don't want to mess it up - take it to a good guitar tech. These sorts of adjustments, unless they are very minor, are not as easy as the youtube DIY videos suggest. Adjusting the truss rod often also requires you to adjust the action down by the bridge, and can also effect intonation, and how the strings sit in the nut.
Good quality modern guitars are carefully engineered precision tools, with a number of related components that interact with one another - better safe than sorry. (I've ruined two basses over the years by messing around with the action and the truss rod.)