Do mudguards/fenders help? If so, what are the best for a fixie commuter? I ride an SE Lager fixed. I'm riding on sealed paths and roads pretty much all of my commute.

On wet days my bike picks up a lot of water and also a lot of sandy/silty residue. It coats the frame and also clogs up the chain a lot. I imagine that my chain life will be suffering because of this.

Has anyone tried running mudguards and seen what kind of a difference it makes? My fixie doesn't have a huge amount of frame clearance around the wheels so I'll need something fairly minimal. I've seen these Crud Roadracers and they look like they have good coverage.

PS: I know that putting mudguards on a fixie is sacrilege (to some people... I'm not in that camp). But I'm running it for endurance and reduced maintenance, not exactly for style.

Update: Thanks for a bunch of awesome comments. However the thing I'm really wanting to focus on is whether I'll get a significantly longer lifespan for my running gear. I have waterproofs and don't mind the mess so much, I'm just trying to reduce my maintenance load and expense. The major areas I see that might be improved is chain (and therefore cogs) and maybe the bottom bracket, if I can reduce the amount of water hitting the seat pole and running down into the bracket.

Update 2: I bought a pair of the Crud Roadracers and, wow, they make such a difference. I rode on quite a wet day, but my running gear and clothes all stayed completely dry. I'm concerned they might not be durable for a commuter, but I'm certainly sold on mudguards/fenders for now.
I have a pair of SKS Race Blades (e.g. from Wiggle). They clip on and off really easily, for washing, security or just for the long days of summer when rain is decidedly unlikely. They are reasonably small and should fit all but the tightest of clearances. 

For all the reasons you mention, I use them - cleanliness of my legs, back, bag and chain - but also because I like to at least play at being a good citizen. On my commute there are lots of other cyclists. Would you prefer to ride in the wet behind someone with or without guards? So the fact I'm being nice to my fellow cyclists is a really cool side benefit. 

And if you think mudguards are sacrilege then, to be honest, you're probably not going to be reading this; style-over-substance hipsters are only dimly aware of the real reasons for cycling, only doing it because they think it's cool. And while it is cool, only not for the reasons they think ...