Some people have it. Some do not. I have taken very large amounts of opiates before and I have never ever experienced nausea from them. I think you are not likely to experience it at lower doses from say, codeine or hydrocodone either, but honestly, it varies by individuals.

It would suck if I experienced nausea, and it would equally suck if I experienced euphoria from opiates, because I have an addictive personality. Thankfully I do not experience euphoria at all from opiates.

BTW I remember having ulcers from NSAIDs before, that is yuck, too. I ended up vomiting blood and I had to be admitted to the hospital. I think I would choose constipation (which can be managed) over this. But yeah, if opiates caused nausea for me, I would not take them for sure.

Ultimately, people should figure out what works for them and stick to it. Unfortunately it might work until it does not, i.e. causes harm. Some people get no ulcers from taking NSAIDs on the daily, and I did just from a few days of taking it (and it was not even naproxen!). :| I am also allergic to metamizole which is the most common painkiller around here (Algopyrin, Optalgin). For my grandma, it seems to work best for her, although she may want to try pregabalin, as her pain is neuropathic (too). She was given tramadol not that long ago and she got somewhat delirious. They probably gave it to her deliberately because she was making a scene at the hospital.