Do SC strategies recommend we write anything down during test?

I've been attending GMAT prep courses in person as well as taking some "Verbal" courses through various online tutorials. Both those courses
lay out "steps" to use when doing SC. An example are the steps below.

Step #1
Read the original sentence and try to identify an error BEFORE looking at the answer choices.

Step #2
If an error is detected in the original sentence, or if the sentence is confusing (i.e. you'd
have to read it again to figure out what it means), immediately eliminate answer choice A and
physically cross it off your scratch paper.

Step #3
If an error is detected in the original sentence, eliminate any answer choice that doesn't make
the necessary correction.

Step #4
If more than one answer choice remains, or if no mistake was detected to begin with (in which case
all five answer choices remain as possibilities):
- Go through your checklist of common GMAT grammar mistakes.
- Look to the answer choices for clues; run the differences through your grammar checklist.
- Apply GMAT Effectiveness Rules

Step #5
After going through the checklist in Step 4, if you still do not detect a mistake in the original sentence, choose
answer choice A.

So my question is, since you have to go through all these steps is it recommended that you write anything down on the provided scratch
paper as you're going through the steps, or are you purely going through the steps mentally?