Several summers ago, I gave a quiz in class, using Moodle, to approximately 50 students that had 40 questions in it. I am quite sure that I was still running my Moodle from a hosted server (similar to Marcus). Of course, I kept my fingers crossed as these 50 students all began the quiz within a 5 minute timeframe. It worked! On the tail end of this quiz, there was more dispersion of finish times as different students completed their quiz at different times. When the two-hour quiz time approached, I think that I had only 5 to 10 students who submitted at approximately the same time.
For a long quiz (like 50 questions), it is recommended to break this down into smaller pieces (like 10 per page) so that when students hit the "Next" button, Moodle will do an intermittent save.
I don't this that in general the number of questions in a quiz affects the server load much. In the Moodle docs, it describes how "concurrent usage" does. So, if you said to all 50 student "Hit the start button right now", that would put a big load on the server.
You might want to consider letting students begin the exam within a wider timeframe. You might say, for example, "You can show up between 10AM and 10:30AM to begin your exam." Yes, your logistics of administering an exam might not allow this.
When I give exams online, I actually have giving students anywhere from one to three days (3 for an exam that spans a weekend) to begin their exam, but then I make these exams be timed so that once a student begins the exam, they only have one hour to complete it (as an example). This allows me to spread the load on my (now, virtual) server.