Originally, “True Romance” was supposed to open with an Elvis Presley number, but Tony Scott didn’t wanna have to deal with getting the liscensing permission from the Presley estate to go through with it, so he had Charlie Sexton write “Graceland”, which is the song playing during the opening credits.
That said, the intentions were always there for “T.R.” The entire film is like a mini-homage to the King. Elvis is also mentioned or referenced to in “Pulp Fiction” (Elvis man…) and “Kill Bill” (Buck’s/The Brides aviator sunglasses).
But, to answer your main question, no. There has never been an Elvis Presley song used in a Q.T. movie except for the accapella version of “Heartbreak Hotel”, as sung by Val Kilmer in “T.R.” But you already knew that…