No. But it could help. But be strategic.
This is some worthwhile reading. I wouldn't take it all as gospel but this was a thought provoking post for me. In general stropping on an un-treated medium really only does so much unless you bring an already clean stone edge to the strop. If you can't slowly draw cut paper towel free hanging, a strop will do precious little.
A CrOx treated strop can help with somewhat larger burrs, but even then the foundation work needs to be pretty good. Your smooth leather is doing even less.
https://scienceofsharp.com/2024/02/03/seven-misconceptions-about-knife-burrs/
When you say strop, the details matter too. Fixed to a board or hanging? Leather (smooth or rough?), cotton, linen, cardboard? Treated or untreated? If treated, with what? CrOx, diamond, red rouge? Any could have an impact on how much abrasive power and how much rounding you're doing at the edge. The sheer number of strokes has an impact on the amount of plastic deformation.
I realize that's a lot of detail but it matters for a trick like this. I'm sure your knife cuts food well. Its primary task.
A smooth leather strop I've found most useful for razors. An edge coming with almost no burr due to how razors are sharpened. I really never use one for a kitchen knife. Because my freehand angles are shakier than a razor, and I'm using coarser stones, I want a strop to have more abrasive power. This means linen, single layer cardboard or a CrOx/diamond treated denim strop.
For a trick like this, I tend to go rigid-back to avoid too much rounding (as opposed to a hanging strop). Rounding increases the effective sharpening angle, making this trick a little trickier. I would try stropping ONE time on each side, cut a paper towel. Strop ONE more time. Cut another towel. Depending on compound and abrasive power, one swipe can do more than you might think. Especially diamond. Going one at a time will help you build an intuition of what's not enough and what's too much.
And the whole time, feel and listen. Correlate those feedback queues with performance. Then re-sharpen and do it all over. Then put it down and come back tomorrow. Take notes if it helps. I rarely if ever look back at mine but writing forces me to think and decide "what did I see, hear and feel" so it imprints on me.
You're clearly eager and dedicated, keep at it!