Gotta love salesmen...
It's just self-adhesive athletic tape. If you want to try it I'd suggest visiting your local dollar store or drug store, cheaper and no shipping. Usually a multitude of colors. My local grocery store carries the same stuff you linked for $1 a roll. Same stuff. There is also realtree printed versions to wrap rifles with that runs about $14 a roll. Cool stuff to use.
To answer your question, since there isn't any actual adhesive to this tape, you may find that the ends don't stay down like sticky tape would and eventually it will begin to un-roll from the handle needing replacement. It will will also build up thicker and quicker than sticky tape because it's a thicker product, possibly becoming bulky and a hindrance. Which is kind of the nature of the beast but at $4 bucks a roll + shipping, I would find a cheaper thinner alternative. That's just my .02¢ and what doesn't work for some may work great for others.
Personally, I use electrical tape. If you wrap a layer backwards (sticky side up) then attach your reel overlapping the sticky pieces, there is no mess or damage to anything. The exposed sticky side also helps hold your reel in place so you can actually attach it and keep everything lined up well. You can also get electrical tape in pretty much any color you want now a days.
