Yes. The codeine is soluble in both; the soluble ones are the big 'uns that you drop into a glass of water and which subsequently effervesce and dissolve. You then have a mixture of water, codeine and paracetamol, which is useless. You want the ones where the paracetamol is insoluble, so it ends up as a chalky lump in the filter while the water/codeine mixture drips through. You need to edit the name of the pharmacy out of that post; "the chemist's" is all the information we need.
The paracetamol is actually insoluble in both. The reason most people think the fizzy ones are different, it because usually most people only take 2 in a glass of water, so it all dissolves. There's also no insoluble fillers, so when you dissolve 32down, it looks like a lot less "paracetamol" than when you add water to crushed pills
Dispersible aspirin is another story. There is a chemical in it that forms a complex with the aspirin, making it very soluble, and unable to be removed by CWE
However there is an insane amount of sodium in each effervescent tablet, approx 400mg's, that cannot be removed, and will box your kidneys if you have any serious habit