I should not be doing this at such a time in the semester, but I kept the screen reader running for a few hours today, and I found, to my dismay, that the answer is no. A system-provided screen reader is not necessarily stable.
The first program to fall victim to instability was Terminal. It started crashing for no apparent reason, and at one point it repeatedly crashed after less than a couple of minutes of usage. Terminal and VoiceOver do not play well together.
The second program to fall victim to instability was Safari. After a few hours of screen reader usage, Safari started to stop responding to tab switching. Turning VoiceOver off immediately fixed the problem. Turning it on caused the problem to resurface after just a couple of minutes.
If such is the stability of a screen reader built into the OS, I wonder what kind of stability third-party screen readers on other platforms can really achieve.