Your description is more or less the "gapped" or "skipped" view of the pentatonic scale which is a major scale with the 4th and 7th degrees skipped or removed.
The reading I have done basically says the pentatonic scale is not derived from a major scale, or diatonic scale. The pentatonic scale is its own entity: a five tone scale with nothing skipped or missing. I think it's believed the pentatonic scale existed long before diatonic scales.
I have only seen the degree names like tonic, supertonic, mediant, etc. shown in the context of diatonic scales. And there are certain harmonic associations with those degrees. For example, the leading tones is associated with dominant harmony, the mediant with the tonic chord.
Obviously you can't complete all the basic diatonic triads with only a pentatonic scale and that seems to be where the mingling of scale degree names in a pentatonic context gets a bit questionable. You could speak of the "dominant" in a pentatonic scale, and most people will understand you mean the tone a perfect fifth above the starting tone (tonic,) but yet you can't really have a proper "dominant" chord, because there is no leading tone, no tone a half step below the starting tone of the pentatonic scale.
I'm not sure if there is an absolute right or wrong about this, but I think you can say the scale degree names are strongly associated with diatonic scales and chords.
To the extent it would be consider a problem to use those names in a pentatonic context, you could simply refer to "1st scale degree", "second scale degree", etc. or perhaps "the major third of the scale", or "perfect fifth of the scale", etc.