I leave the radio on for Sweet Pea. I have it plugged into a timer, and set the timer for off times so she can have some quiet time as well.
Yes, I do think it helps them learn words and all parrots seem to love music.
My daughter was home once during a weekday and using the computer that is located in the same room as Sweet Pea. My daughter told me that as a certain song was coming on the radio, that Sweet Pea started singing to it, word for word.
I've never heard Sweet Pea sing along with the radio... so it fits with my thinking that parrots will vocalize in certain ways and at certain times, differently than you might expect. Such as you might try your hardest to teach them a certain word or phrase, and never hear them say it... yet someone else will hear them say it. LOL