Grasses and "weeds" do uptake soil nutrients but whether it would be enough to adversly affect fruit trees is highly debatable. Some orchards around here have "clean" soil with no grass or "weeds" evident, but most have grass growing in the orchard along with the trees and that grass is mulch mowed right back into the turf where the grass clippings can supply some nutrients to the soil.
Heavily mulching around the tree trunk to aid in suppressing grass growth there can help make mowing easier, but constantly spraying plant killers to control growth would not be an acceptable organic proactice.

If you are concerned about the grass and weeds taking up nitrogen that would otherwise be available for your trees, why not over plant these areas with clover which will fix nitrogen into the soil for your trees to use, provide a habitat for beneficial insects, and provide a food source for the bees?

You might want to consider putting a heavy layer of organic mulch around each tree, with the mulch circle beeing roughly the diameter of the branch spread of the tree.

This will not only control grass and weeds, but fertilize the trees and slowly add organic matter into the soil. Any fruit or leaves that fall can just be left there to become part of the mulch.

Ron
The Garden Guy
http://www.TheGardenGuy.org

In Florida , we keep weeds and grasses away from our citrus trees . This is primarily because citrus are highly susceptible to foot rot and root rot from fungus . Peach trees probably do not have this problem due to a different type of root system .
Mulch sounds like an excellent idea - just keep it away from the tree trunks by about 4 to 6 inches .
Check with your local Extension Agency . They have plenty of info on organic farming and advocate the practice of using " earth friendly products . "

There's a peach grower near San Antonio who piles mulch down the rows between the trees. His mulch is on the order of a foot or more high. I got the impression the mulch extended from canopy to canopy but does not approach the trunk of the tree. With that much mulch even in Texas he does not have to irrigate.

I did not get a chance to talk to him but I would wonder about thinning and picking the fruit with that much mulch.

Is "orchard grass" for orchards? Or is that just a marketing name?

Orchard grass is called that because it is a grass that will "invade" an orchard a little ways. It tolerates light shade while other forage type grasses do not. It is very tasty to cattle.