Answer: It appears to function normally, but performance suffers drastically for any compute-intensive operations such as resizing images.
I had two raspberry Pi 3s (same model etc) running the exact same software (flashed both SD cards with same image). One of them was powered by a 1A supply, the other by a 1.5A supply.
When I ran a Python openCV script which ran some very simple openCV operations such as resizing and blurring an image, performance difference was a factor of 2: the raspberry Pi on the 1A supply ran at almost exactly (+-2.5%) 50% of the speed of the Pi on the 1.5A supply. Switched the power supplies and the performance difference was reversed. The 1A power supply was an Apple 5V adapter.
It should be noted that aside from the performance difference, there was no perceivable difference in functionality. I was able to SSH in and run commands just as normal. No bugs or glitches were experienced. It behaved exactly like a normal computer (just a bit slow).
Will update with more details once I get the official 2.5A power supply.
UPDATE: The 2.5A power supply does not seem to make an appreciable difference in performance compared to the 1.5A power supply, at least not from what I could see from the Python openCV benchmarking program I ran (single-threaded). Perhaps there might be a noticeable difference once I connect up more current-drawing components or use multiple cores? I’ll leave these questions for future work.