We don't use it that way in American English. If I describe something as shabby, it means it's worn or well-used and suggests it needs to be replaced soon. Shabby clothing might be stained, threadbare, or torn.

Sometimes attempting to be frugal can lead to the purchase of something shabby, but I would not say they are the same thing. When something is frugal, it saves you money. When something is shabby, it is of poor quality (usually falling apart). Hope this helps :)