Yes, the paper towels will be wet if there is a leak but if there is a leak they will get soaked over time with a very small leak and you might not be able to tell exactly where the leak is. If you do a visual check while you fill it with water it is evident with food coloring. Let me give you an example. We had a leaking toilet where the tank bolts onto the bowl. I'd wipe it and it was such a slow leak I couldn't tell exactly where it was coming from. The logical conclusion would be the large gasket where the tank and bowl fit together. I went online and found this solution.
I flushed it then tied the arm up so it wouldn't refill. Then I thoroughly dried the wet bottom and let the water refill it while I added food coloring. Guess what? It wasn't the big rubber gasket after all, it was one of the four small bolts that held the tank to the bowl. I watched with a mirror and a small red stain started coming from one of the bolts. The small rubber gaskets had rotted on that bolt and the telltale red liquid showed me exactly where the leak was. Had I removed all four bolts and replaced the large gasket and not noticed the flattened out condition of the four bolt washers, it would have still leaked after all of my trouble.
But I would have seen the flattened out, hard condition of the small rubber bolt gaskets and it would have at least mean't another trip to the hardware store. If I hadn't done this and not replaced them, all of my work would have been for nothing. Threaded joints need a generous wrap of teflon tape or they will leak, it will be a very small amount, just drips which won't amount to much but I agree, the main concern is where the liner meets the seal.
