More or less, yes.
When you slide the creature's statistics by n-many rows to a row of a higher CR in the Monster Statistics by Challenge Rating table in the manner you've described (including all of the statistics covered by the table, not just some of them), the practical effect on the CR calculation is as follows:
- You increase the offensive CR by n-many rows in the table.
- You increase the defensive CR by n-many rows in the table.
- Thus, you increase the average CR by n-many rows in the table, since the average has increased by (n + n) ÷ 2 = n-many rows. This new average CR is the estimated CR of the adjusted monster.
- Since each of the n-many rows increased the CR by exactly +1, you've increased the monster's CR by +n.
The math is reversed when sliding to a row of a lower CR.
Then, barring any independent balancing steps you as the DM might deem necessary due to "game feel", the math should work out correctly. These "game feel" assessments should occur when crossing between CR's 4 and 5, CR's 10 and 11, and CR's 16 and 17, corresponding to the boundaries of the player tiers, due to conditions, spells, or instant death effects that may be impossible to deal with at lower levels or trivially easy at higher levels.
Most published monsters seem to involve some amount of "game feel" balancing based on designer's intuition or playtesting rather than following the calculations directly. (This is why there are so many questions on RPG.SE asking for CR verification for specific published monsters.) For that reason, you shouldn't feel beholden to the math regarding the CR calculations; they will always be nothing more than estimates. Most of these "game feel" adjustments can be intuited by checking the Monster Features table later in the same section, and you should confirm that your monster doesn't have a feature with a tier-dependent adjustment in this table (such as Relentless or Undead Fortitude) or else take that into account if it does.
However, with the process you describe, since the effect on the math should be negligible and since the published monster has already included any "game feel" balancing the designer thought necessary, you should end up with an adjusted CR that isn't problematic, pending your own "game feel" assessment. Meaning, your process should give you a reliable CR with very little effort, even if thorough playtesting might "game feel" it to be 1 or 2 steps higher or lower.
In addition, I have used this same process for many homebrew monsters at my table and have never had a problem with it, so in my experience the technique is safe and effective. It's an excellent DM's tool for minimizing prep time; you might only use this adjusted monster once or twice, so it's not worth your time to spend hours making it "publish-perfect." Note that this technique is best when used to scale up rather than down: it's not a big deal if a monster ends up being slightly too easy, but it could be a really big deal if a monster is too hard at lower levels, and small differences in CR are much more noticeable at lower levels than higher levels.