Well, there are a couple of different things that cause a "band aid" taste. One is chlorine/chloramines in the water. Another could be infection, and finally a stressed yeast/ hot fermentation can also cause it.
If it's mild, and caused by stressed yeast, it might improve. If it's from chlorine, it probably won't get much better but won't get worse. If it's from infection, it'll get worse. Depending on the cause of this off-flavor, it might become drinkable with some time but never beer very good in all probability.
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