The filter doesn't get rid of all the chemicals. Sun tan oils can contain some products you do not want to ingest. The pocket filter has a floater. Sun tan oils will float on top typically, so you can easily avoid the oils.
Swimming pool water contains chlorine, which this does not remove. You would need to run it through a carbon filter to remove the chlorine. Katadyn has an add-on carbon cartridge that will work for this.
I think it would work for swimming pool water, meaning chlorine, sun tan oil? I have no idea. Are they bad. Yes, but I would guess that depending on the size or your pool the water to oil ratio would be so low it would not harm a full grown adult. I would refer you to Kayadyn's website to ask these technical questions.
Since you can disassemble the filter and wipe it down, I doubt the small amount of suntan oil from a pool would damage it. Just don't know why one would want to filter and drink their swimming pool water.