Firstly, to adress the cycling question...yes and no. Your cycle will be set back a little since you will be getting rid of the beneficial bacteria in the filter. BUT most beneficial bacteria live in the gravel, so this shuldn't be a huge problem.
Secondly, if you are buying this filter from Wal-mart, I am going to guess it is a Tetra Whisper filter. You probably just got a defective one. I don't like the Whispers much because the media slot is small, but to each his own. There are tons of thread on which filter is best on this forum if you look around. I reccommend a Bio-Wheel; others will tell you to go with Aquaclear. Both are good options.
Thirdly, in a new tank like yours where the filter doesn't have a lot of bacteria yet, shutting it down probably won't hurt it much. If you have an air pump with a stone or anything like that, keep it running just to improve circulation.
Bottom line, your tank isn't going to do anything without a filter that it wouldn't do with one at this point. If you were asking about algae thinking that it would grow in the time you are at Wal-mart, then don't worry about it. Your filter isn't doing anything to get rid of algae anyway.
*Edit: Just so you know, you should be doing 25% water changes every week regardless of how many fish you have and especially since you have a bit of a crowded tank.