Question

If tachyons existed, would we notice them?

Answer 1

The problem is, that the word simultaneously means that the events are light-like connected. So, the flashing of two lights on your ribbon is not a space-like event.  Tachyons behave very peculiar, i.e. in such a way that they lose energy while accelerating. It takes more and more energy to asymptotically slow them down towards the speed of light. It can never be stopped and thus has no connection to (no interaction with) our side of the barrier that is the speed of light. Therefore the answer is no, we can never notice them, even though they might be there (some string theories have something to say about Tachyons).

Answer 2

the underlying geometric notions: how to define/measure "velocity" (or at least: "average speed, from starting gate to finish line"), "distance" (such as "between starting gate and finish line", or whether they are "at rest" to each other" at all), "duration" ("from start, to finish"), or what constitutes a "signal relation" (let's say "from the starting gate indicating the start to the first indication of the finish line taking notice"