Answer:
No. That's false.
Step-by-step explanation:
Phonemes are distinct units of sound in a language that distinguish one word from another. It's what distinguishes the meanings of words. They are both vowels and consonants.
bad vs. dad / cat vs. cot
Allophones, on the other hand, are the different pronunciations of phonemes, but they are not phonemes because they do not change the meaning of the word.
Consider the word 'butter'. Some native speakers will say [bʌɾə] (budder). Others will say [bʌtə] (butter). You can see here that [t] and [ɾ] are allophones of the same phoneme. Whatever way you say it, the meaning of the word does not change.
We Texans proudly say 'budder.' :) :)