Short answer: Yes, Vader occasionally lifts someone when using Force Choke, but he didn't do so in any of the films.
This Youtube video is a collection of every scene in which Darth Vader used Force Choke on someone in the two trilogies:
Wookieepedia's article on Force Choke lists the same instances for Vader (it also lists some from his time before he turned to the dark side and became Vader). Vader used Force Choke the following times in the films:
- Against Padme in Episode III.
- Against Admiral Motti on the Death Star in Episode IV.
- Against Admiral Ozzel at Hoth in Episode V.
- Against Captain Needa after his failure to capture the Millennium Falcon in Episode V.
As the linked Youtube video confirms, Vader never lifted anyone off the ground with the Force when using Force Choke in the films.
That said, Dooku lifted Obi-Wan off the ground when choking him in Episode III:
Also, some more recent works portray Vader as lifting a victim off the ground while using Force Choke. For example:
Without breaking stride, he used the Force to take hold of Orn Free Taa. He lifted the obese Twi’lek from the floor and hung him in the air before the Emperor. Taa, wide-eyed, his many chins trembling, pawed at his throat and gasped for air. Vader took care not to kill him...yet.
- Lords of the Sith (published in 2015), p. 99
The concept of lifting a person off the ground when choking him/her did come before the prequel trilogy. For example, some (now Legends) video games have a dark side power (sometimes called Force Grip) in which the target is lifted off the ground. For example, from Jedi Knight II: Jedi Outcast:
This is probably where the idea of a levitating Force Choke originated from. The games may have been inspired by the combination of Vader's propensity for using Force Choke and the fact that he lifted the Rebel on the Tantive IV off the ground (albeit physically) in Episode IV. The inspiration may also have been a combination of normal levitation (of lightsabers, X-Wings, etc.) using the Force and Force Choke.