There are different sized filters- .5 microns and .2 microns that I know of. The coarser filters wouldn't filter out all of the yeast, but the finer ones would.
Yeast are in suspension, sugar is in solution. If you define completely filtered as removing all items from suspension then you would have no yeast. Commercial breweries that bottle condition typically remove yeast via filtration or centrifuge and add fresh yeast before bottling.
For a home brewer I imagine it would be either pretty difficult or expensive to filter out all of the yeast. Surely, if you managed to filter out some then there would still be plenty to carbonate the beer.
Why do you want to filter your beer is the question. Time and patients will do the same thing and leave you with a more delicious, more authentic beer. If you naturally carbonate your beer there is going to be sediment in your bottle no matter what. Filtration will not solve that.
If you were trying to turn your beer around quickly, I guess you could use a coarse filter to remove a good bit of the yeast and still have some left to bottle condition the beer. I've never heard of anyone doing this, but in theory it would work.
Just let the beer clear in the fermenter before you rack to the bottling bucket. You'd have to move it to a pressure vessel like a keg to be able to push beer through a filter anyway. You weren't thinking you could gravity drain through 5 micron right?