I have picked up barrels several times and can assure you it works.
In my Honour mode no reload run I only got 1 because I forgot you have to click on the further away one first, but you only need 16 ST to pick up 2 I've done it on reload runs before, Telekinesis and Haste are only needed if you want all 3.
Here's footage on my semi failed attempt, maybe somebody not doing it perfectly and still getting one barrel helps you more than a speedrunner doing it:
https://youtu.be/U5iJbOOzumQ?t=1704