Can bugs bite through Noseeum when it is in contact with skin?

Mosquitos can.

Don't know about bites, but skeeters can still get through it (and many thinner single-layer solid fabrics).

[On edit] Looks like you beat me to it. I started typing, then let it sit for a while. In case you're in a cave, there's a news conference on now announcing Bin Laden is toast.

Yes!

Skeeters and blackflies can bite through pretty much anything that's in direct contact with your skin, but I was also planning on trying something like you are, Brett.

The trick I'm going to try is treating the bug netting with permethrin. Bugs can't bite through anything when they're dead.

Yup. I tried the Sea to Summit ones, they left my hands badly bitten. Same for all the small nets. Unless you have a space between the netting and your skin, they will feast. A high density weave will put off black flies. They seem to require about .01" or more (~a hundreth of an inch, depending on the species) of space to bite through. The ones we get in the ADK's need more like .02" or around 1/64". The proboscis of a Mosquito is up to a 1/4" long and very fine and can bite through things black flies cannot. Both are out in the ADK's. Later on the "punkies" or "noseums" are out. These can bite through untreated nylon, let alone mesh. Deerflies don't usually bite through things. They like open skin to perform their blood sucking.

While hiking I've often watched mosquitoes trying to get to me. They will land and then repeatedly poke their biting needle toward my skin, trying to get through whatever clothing is covering the skin. So they will, through trial and error, eventually get through a loosly woven or knitted fabric or mosquito netting that is right on the skin.

In the Pacific Northwest I have found that they can not get their needle through tightly woven 1.9 ounce nylon, however. Even on a section tightly stretched over and against my skin (i.e. wind pants on my thigh) they will poke and poke and poke but not get through.

Yeah, what Daryl said. Wind clothes work well for bug protection.

A much heavier approach is the Original Bug Shirt: http://www.bugshirt.com/
You'll notice that none of the netting touches the skin. The suit works well, as long as you keep things lined up properly (if you shift your shirt around accidentally you might have the mesh touching your skin).

I am close to bald, and in Greenland with a buff on my head and a nanoseeum headnet, i was bitten through both of them , not once… my head was covered with bites.