There is no way to be 100% sure about this, but personally I think it can, but I highly doubt it is a major factor. Here is my take on it (strictly opinion/educated guess):
I don't really think it is random at all, but actually extremely calculated. This is because Jagex's detection system is based so highly off of statistics. I would guess that 98% of randoms go to legitimate players while the other 2% go to expected bots. Now, most of the 98% will either do the random or click "dismiss" (but not all), while most of the 2% will simply ignore it. Knowing that almost all of the people you test will be clean, you can then gather data on what that person is doing and how they are doing it, reaction time to the random, etc. Out of that 98% who are expected to be legitimate players, you can then break it down into skill type, afkable, click intensive, or somewhere in the middle. More than likely, the 98%ers who completely ignored the random were probably doing an afk skill such as fishing, while the 98%ers who dismissed/did the random were probably doing something click intensive. Taking this data gathered from the 98% Jagex can then compare it to the people who fall into the 2% category.
This alone will more than likely not be the deciding factor between you getting ban or not, but rather be a potential red flag for Jagex to take a closer look at your account. This is where the statistics come into play. If you are in the 2% and fishing, well that is an extremely afkable skill, so you automatically have a higher chance of ignoring it. But if Jagex sees you have ignored 5 randoms in a row then notices you have been playing for 20 hours straight or in a perfect/extremely similar intervals non-stop, then that will raise another red flag.
TL;DR Version:
I believe Jagex uses statistics/data gathered from "random" events to raise a red flag on an account that is potentially botting, thus Jagex will decide if the red flag is worth looking into or if they will just look past it. Random events alone will not be the deciding factor in a bannable situation.