The more methods you call (which is what you do with a plugin or module tag) the longer it will take to process it. So, as Eric said, yes. It will affect performance when you compare it to omitting it altogether.
However, it's never as black and white as this. The amount of time a tag takes to process differs. It depends on all sorts of things. In the case of Widon't, it's just a simple string manipulation, so that hardly takes any time at all. Other plugins/modules might query the DB, and that can be a much, much bigger impact on performance, especially if no caching is applied.
But, in your case, it shouldn't matter all that much. It will be hard to tell the impact, if noticeable at all.