Do side effects reduce the double blind aspects of a medical study?

The most beneficial studies of the effects of a new medicine or vaccine are generally placebo-controlled double-blind. What double-blind means is that neither the doctor or the patient knows whether s/he was injected with a placebo or the drug. However, if the drug causes readily observable side effects such as “injection site pain, fatigue, myalgia, arthralgia, headache, and erythema/redness at the injection site”, while the placebo obviously does not, don’t the doctor and patient know what the patient got?

Does this knowledge possibly influence a patient’s actions?