Tuplets can transform a rhythm into an irrational (or irregular) rhythm, but how do we precisely define a rational rhythm in the first place?
First off time signatures can be irrational or rational, but rhythms however cannot. Rhythms can be irregular, but that's not the same thing as a meter being irrational and is better described as syncopated .
Whether a time signature is rational or irrational depends on the denominator of the time signature. Any time signature where the denominator is a power 2, for example 2, 4, 8, and 16, is rational.
What this means is the underlying beat is a typical note like the half, quarter, eighth, and sixteenth .
An irrational meter has a denominator that is not a power of two. This is rare, but can happen if you use a lot of tuples like you said. For example if you let the quater note triples get the beat in a time signature you'll end up with a 6 as your denominator and however many quater note triples you have per measuer is the numerator. For more explication on other examples of this, see this answer.