This touches on the quantity-quality relationship. Since dissertations have to be supervised (and even co-supervised), much depends on whether an increase in the number of graduate students goes hand in hand with a commensurate increase in the number of supervisors (staff-student ratios are usually set by quality assurance agencies). And with a commensurate increase in whatever facilities are needed (e.g. computers, labs, seminar rooms). Secondly, are we assuming that all students are interchangeable in terms of their quality, and the same for the supervisors? So that any pairing of student and supervisor will produce the same amount of output quality? For the answer to be "no", I think we have to make a lot of assumptions. Only a quantitative change that does not affect the character of the entire dissertation process (including the administrative context) would support a "yes" but that's unlikely.
Yes I am sure numbers are a factor but perhaps a better question is what are the critical factors for determining quality in masters and doctoral programmes?
I agree with Antoon De Rycker that supervision is probably the most important factor. There is also the expertise of the supervisors, the ability of the students and the quality of the research methods teaching.
By the way, I am currently coordinating over 250 undergraduate dissertation students and over 80 masters students, and providing research methods training to a small group of doctoral students.
Yes, supervisory practices are critical to completion.
By the way, what's your view on the master's thesis? To me, it's more of an "exercise" in which students provide evidence they understand the research process (relevant to their discipline, topic area and questions) and how to apply it rather than a sort of "opus magnum", a piece of solid, original, high-value-added and publishable research. There are, of course, exceptional students who can do more but it's a relevant question to ask as the way we conceptualise thesis research at any level has an impact on how much supervisory skill and work are required.