The answer is yes, but not as commonly as one might suppose, or even as is reported, especially regarding the severity.
At its most accurate, the statement is hyperbole, but in the vast majority of complaints I see, there is little-to-no actual anhedonia present. Although the majority of patients seem sincere, when a patient tells me they are "completely numb" or feel "like a zombie" on a starting dose of an SSRI, the situation is invariably one of unreliable reporting (as opposed to those patients who complain of specific anhedonic symptoms, in less absolute terms).
Many are patients with anxiety-spectrum disorders who are concerned about this possible side effect, which they have previously read or heard about, and their anticipatory anxiety ironically leads them to declare the global annihilation of all emotionality on what amounts to very low, starting doses of serotonergic medications (or upon the first dosage escalation), all evidence to the contrary.
Others are reluctant to submit to an adequate therapeutic trial of an SSRI (or similar agent) for a variety of other reasons: other, more likely, side effects, including and especially sexual dysfunction, a particular anhedonic side effect that does not rely on the complete numbing of emotionality to manifest, nor to threaten to derail treatment. Significant sexual dysfunction is understandably a dealbreaker for many patients, but many individuals choose to not be upfront with their provider; for some, it may be easier to claim global anhedonia.
Severe anhedonia is not uncommonly seen in major depressive episodes as a symptom, but as a side effect, medication-induced anhedonia tends to be mild-to-moderate, and easily reversible with dosage modulation and/or the addition of dopaminergic agents, especially when the latter are indicated for other reasons.
In every case, it is incumbent upon the clinician to discern reliable reports from those that are over-endorsed; to determine the reason for these distortions; whether or not the patient is consciously aware they are misrepresenting the situation; and how best to move forward, either to preserve the trial, or else to abort, but in either case only after engaging in an open, honest and accurate risk/benefit analysis with the patient.
p.s. craving brains is a highly sensitive indicator. Happy Halloween!