In trials not really since all participants in trials must sign an informed consent form and in that process are informed of the details of the trial's objectives and possible outcomes, including the fact that they may receive a placebo, assuming a placebo is used in the trial. Nocebo is more often investigated retrospectively for ethical reasons.

I don't doubt that some people who didn't want (e.g.) a COVID-19 vaccine but who had to get it to keep their job (or for whatever reason) may well have experienced more side-effects than others. But this is where it gets complicated, cos some people who didn't want the vaccine, say, because they heard other people became ill after getting it - then they get it and are psychologically determined to not feel ill, cos they're "not a pussy" or whatever. But such people may still get destroyed (temporarily) by post-vaccine flu-like symptoms because ultimately individual genetic/metabolic variation is a stronger determinant of treatment response than psychological disposition (but it's not always as simple as that!)

Edit: this is a very interesting paper on side-effects in vaccine placebo arms:

https://jamanetwork.com/journals/jamanetworkopen/fullarticle/2788172#:~:text=The%20ratio%20between%20placebo%20and,51.8%25%20after%20the%20second%20dose.