In the vast majority of cases, no. But sometimes I think the answer is slightly more complex than that. My analogy is this: If there is a black MD and they are not a strong doctor, do you think there is going to be a small population of people, both patients and other physicians, who are going to ascribe some of that weakness to the color of the patient's skin? That they were an affirmative action admit to medical school or that blacks aren't as intelligent as whites? But would the vast majority say to themselves something along the lines of: "I've seen crappy white doctors and crappy black doctors (along with good from both), this just happens to be one of the bad and I can't judge all by this one."? In general I'd venture to say that, unfortunately, intellectually invalid judgment based on skin color is far more common than based on degree type, at least from a patient perspective, because 1) at some places (not all) the degree type is not as prominently displayed as "Dr." (the equalizing word in patients' minds) and even if it is 2) The title "Doctor" tends to trump all. Look, I know this is only my exampe, but I have never had any issue with my "DO". I've deliberately had it embroidered on my coat in the past and, at my current large allopathic quarternary care center, it is printed in large font on my ID card and it's on my business card that I hand to all my patients. Never once has anyone had an issue with it. In the four years I've been out of medical school I might have actually reached all the fingers on one hand the times I've been asked about what "DO" meant and it was always a matter of pure curiosity and never a matter of questioning credibility. If it was in the context of a patient-doctor (or if I was doing an echo to help our sonographers) interaction I was always still the doctor, they just saw the opportunity to ask a harmless question. Being asked this has never been a burden (esp. given the number of times it's happened) and if given the time, I enjoy talking about it. At minimum it's an intersting history lesson. (BTW my med school white coat had a huge honkin' DO on it and I didn't get asked about it too many times then either).
If you are a crappy doctor, you will be noted as such by your patients and colleagues, but most will ascribe it to your inherent crappiness. If you're a good doctor who pulls your weight, to other physicians you will simply be known as "colleague".