How important is it to filter out frequencies that a speaker cannot reproduce?

If say, a mid-range speaker has a range from 1k -> 5k, what will be the effect of feeding it a full range (i.e. unfiltered) signal rather than filtering out the sub 1k and >5k frequencies? Would it noticeably adversely affect the audio quality or would the speaker act as its own filter and simply not reproduce those frequencies outside its normal response range?