No. I use the carbon filter for the water and then, after removing the carbon filter for the sediment filter and then sanitizing the whole thing, filter beer into secondary or whatever you go after that. And it is not a paper sediment filter that you use with the 10 inch filters like this, it's a spun polypropylene filter- basically the same as the ones that come in the box with these units (if yours does) except a much finer filtration. The one that came with mine was like 20 micron or so. The carbon filter doesn't usually come with these standard.
Not that I have started with this procedure yet (will do it in a couple weeks) but all the info I've gleamed from others on this site has influenced my purchases. A 3 micron sediment filter is probably the best. Morebeer stocks them. Some guys actually reuse them too by running them in reverse with a sanitizer solution. Not sure about that one yet, but they say it works for them. Seems risky to me in that they are like $3 each and recyclable. Better to just wait to filter a bunch of beer at a time (requiring you to have adequate quantity storage, but..).
I have my filter on 3/4" quick disconnects (mine happen to be tri-clamps, but whatever) so that I can easily remove from my "water in" assembly for filtering beer.