1) Filtering through a screen probably won't work that well. Even if it did, straining a carbonated beverage through a fine mesh would agitate the liquid so much that you'd probably lose the bulk of your carbonation and wind up with something fairly flat.
2) Off flavors can be produced by yeast sitting on the trub for extended periods which was one of the reasons why people used to use secondary fermenters consistently. Generally speaking, the off flavors don't start getting produced until after about a month (general estimation), because most people only ferment for two to three weeks on normal gravity beer, that's not too big of a problem, but I bet it would be for you.
I'd say do it because it would be fun, but I predict a cloudy, flat beer (if you strain it), that tastes a little funny.