That is indeed the whole process. Little to no Tylenol will be left in the solution.
But-let me say this- if you are only planning on taking the 1200 mg dose once, just take your pills. The daily recommended threshold for Tylenol (paracetamol/APAP) is 3000 mg. Until very recently it was 4000 mg. That is on a daily basis, saying if you took 3000 mg per day you'd be fine.
The reason I say this is because doing a CWE with a small amount of pills is 1. ) not necessary and 2.) going to lose too much of the codeine than it's worth.
Basically you are losing codeine for no reason
I applaud the fact that you are concerned about harming your liver. And while this is indeed a harm reduction site, I also feel that sometimes it can be taken to an unnecessary extreme. People take up to 4 plain Tylenol a day no problem. They are either 500 mg per pill or the newer 325 mg per pill. Either way it's over 1200 mg. That is a pretty normal dose to take in a day.
Now, if you are dosing over 3000 mg per day then doing a CWE is a great idea as to not make your liver process all that Tylenol. But from reading your post it sounds like you are just taking the pills today, after having taken some yesterday. (Sounds like you took maybe 3 pills yesterday with about 300-325 mg Tylenol in each and want to take like 4 pills today with about 300-325 mg Tylenol in each) That's really not a big deal. Just take your pills normally.
Now if you start taking more pills where you would be dosing more than 3000 mg per day of Tylenol, by all means do that CWE, it'll protect your liver!
But if this is just today (1200-1300 mg Tylenol) after yesterday (900 mg Tylenol) then you really would be wasting your active ingredient (codeine) by doing a CWE. Because you will not get 100 % back of the active ingredient (codeine). That's not a big deal when doing a CWE on 10/15/20/or more pills, but on 3/4/or so pills it is a bigger proportionate loss
Again, good thinking to be safe. I just think in cases like this that it is going to an unnecessary extreme, and losing your active ingredient for no real benefit. Like when I see these threads "I have 2 Vicodin pills (5mg hydroxide/325mg Tylenol per pill) how do i do a CWE?" I kind of cringe, because while at least the person is reading up on harm reduction, they are taking it to an OCD level. If you were going to take a couple Tylenol for a fever or headache you would take up to 4 pills (325 mg x 4) without thinking twice.
Anyway, you're fine to just take your pills. If you must do a CWE, yes, that is the process just filter using coffee filters or even an old tshirt. Crush up pills and dissolve in cold water and filter. Those are the basics, you can find step by step thorough guides, it'll get out most of the Tylenol but you will lose some active ingredient also.