I typically use cardboard. It decomposes nicely after time. So I don't know about carpet. but you might want to look at these links for other ideas:
http://www.homeorchardsociety......tum/?id=47
http://www.homeorchardsociety......rticle/18/
Hope this helps. 
The natural carpet underlay we use at home actually prevents alot of moisute entering the soil which isn't great. We have it laid in wide stretches to kill weeds in preperation for beds. It is going down a slope so that also may have something to do with it. I imagine it would be good as a weed barrier in smaller sections around maturing trees. During conservation work we have always used cardboard and newspaper with straw. Let us know how you get along if you do choose to use the carpet underlay!
oh yes! I also wanted to mention that sawdust can be detremental if it has been left to dry out or if it is fresh, I cannot remember which way it works. I know that the carbon compounds within the wood require nitrogen from the soil to decompose thus taking it from your trees. This perhaps is only relevent with gum trees and the like. i am in Australia.
I did use the carpet as weed barrier and covered it with about 5" of free sawdust from a neighbor's cabinet shop, mostly from hardwoods. This seems to hold moisture much better than going without any mulch. We don't get much rain from July 1 through September 1 in my area and I water very sparingly. I put the carpet around my grapes and rhubarb. The carpet was the jute-back type (not the rubber back type) so water will flow right through it into the soil, I threw away the padding. I put the carpet upside down. The rhubarb is doing much better this year than last year. Last year the plants were completely died off and dormant by this time of year. This year they are still flourishing with thick stalks and huge leaves.
I don't believe that applying sawdust removes nitrogen from the soil unless it is mixed into the soil, it will tie up some of the soil's nitrogen but only at the contact interface. Eventually, after years of mulching, you will reach an equilibrium of released nitrogen vs. nitrogen tied up by the decomposition. The first year may show some detrimental effect but later years will be beneficial.
The sawdust seems to be less resistant to weed growth than the bark dust that is used more commonly around the Pacific Northwest. Grasses and Buttercups are able to grow in the saw dust if kept moist.
In another area I used some old green shag carpet as weed barrier around newly planted grapes. The carpet was laid right side up and looks like green grass from a distance. It really helped to keep the grass and weeds down for a perimeter around the grape to reduce competition and retain moisture.
Honestly I haven't tried it yet not seen some doing it. To avoid some weeds in my garden, I cover them with big cardboard. That is easier for me to clean. Remember that we usually water the plants morning and afternoon, so it is another task for us to place and remove the carpet before and after watering.
Almost all carpet is synthetic and therefore made of petroleum, binders, and other nasty synthetic chemicals. I don't think that it is coincidence that American cancer rates have skyrocketed over the past few decades. In places with an agricultural lifestyle and no "modern" pollutants, cancer essentially doesn't exist. Brown cardboard without a lot of glossy color covering is wood pulp, really. If you are getting too much carbon into the soil, just apply some urea to the area. Easy to do if you're male. 
John S
PDX OR
Idyllwild
simplepress
jafar
Marsha H
Viron
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