*** Disclaimer **** This is a best guess.
That said, The outside shell is a ground just like the bottom. If the wrap is missing near the TOP of the battery (the positive side) then that could be trouble because it would be easy to short the positive side to the negative side by just bridging the gap.
Also, tape is not a bad idea IF (and check this) it doesn't cause problems with venting. In other words....there's already discussion in ECF's e-cig safety guidelines about batteries that vent getting hot (of course) when they do and SWELLING UP blocking off the tube and thus making the vents useless. Adding a layer of tape could make the diameter of the battery bigger and make this blocking effect more likely.
So if you do add tape, make sure that it isn't too thick. Like one layer. This is particularly true for tube mods that vent out the bottom. I use box mods (have both mechanical and regulated box mods) so I would add the tape in my case.
An easy way to check ...if you have a multimeter...is to do a continuity test on the negative end and the side where the wrap is missing. I don't have those batteries and so can't tell from your pic if that's the negative end (but I assume so for this post). If the test is positive then I'd assume you just have a "big fat negative end" on the battery and not worry about it.
If that's the positive side....I'd worry and tape it. Also, IDK what battery it is specifically. It may be safer chem but IDK since it doesn't show and you didn't state exactly what one it is (like make/model, not just size).
That also assumes that if it's a protected battery the PCB is located on the top (positive) side and the wrap is missing on the negative side..
You can ask the vendor too.
These are all ASSUMPTIONS. I wish I had one to do a continuity test with. Maybe one of you with a multimeter can test one. I know that there's a metal ground strip running down the side of the battery for protected batteries and I assume there's at least some contact with the shell.
Just random thoughts and
