Correction - it really depends on the filter. If it's equipped with activated carbon or whatnot then it will really clean up. If you suck up the yeast it will get clogged and require backflushing etc.
Here is a decent thread on it from another forum:
C
arbon filtration
And here is the wiki on filtered beer:
Filtered beer
I remember seeing a special on brewing beer - not brewmasters - and it showed the breweries filtration system - after every batch they had to take it apart and give it a good cleaning. This is large scale of course and slightly off topic.
Fake edit: it was Dirty Jobs with Mike Rowe.
Edit: Either way, come back and tell us how it turned out.