If you are careless, possibly. If you are careful how you go, fill the flutes in the tap with grease to catch the chips, unwind it a few times during the operation to clean them out and apply more grease, hopefully not.
Or you could get more than a bit OCD about it and completely strip the engine to bare cases.
I had a similar issue. There was just enough grip to get the plug barely "finger tight". I ended up putting a thin bead of RTV on the shoulder of the plug, being careful to not get any on the threads, and then put it in. There was no leakage for the next 1,000 miles. I sold the bike before doing another oil change (and yes, I told the buyer about the issue!).
If I had kept the bike, what I would have done was go to the local auto parts store (I'm in the US) and get a replacement plug with an expandable rubber seal that they make for just such situations.