I've done some extensive reading online after running into this issue to no avail.

I believe the smoke to be present under all driving conditions but most prevalent during idle. The color of the smoke is white, it does not smell/taste wet or sweet and my coolant level has remained the same. It's not sooty nor black so it's most defiantly not fuel. It does not have any tints of blue nor does it even smell like burning oil.

I've installed plenty of headers, both cheap ebay stuff and extremely expensive name brand stuff. Obviously all new headers or in the case a down pipe, will smoke briefly after you've first installed them. This is not external, and it's been persistent for about 200 miles.

I have deleted the SAI system, and kept the PCV system. With high hopes, I removed the PCV system in-case it had failed and the CAT had previously been masking the smoke. No change. My engine is currently check valve free and both the valve cover vent and block vent are open allowing for blow by gasses to escape there. No smoke from either vents, only from the tail pipes.

I also believed prior to removal of the PCV system that the likely-hood of the catalyst removing this level of smoke was slime to none.

It is important to note that the down pipe is wrapped in DEI heat wrap, and that prior to installation of the down pipe I had a P0420 catalyst efficiency code. Removal of the catalyst, a visual inspection confirmed that the cat, most definitely, had melted down, most likely due to the infamous failed 1.8T coils. When I bought the car it was misfiring like crazy, and the previous owner was still driving it 30+ miles a day for work. Since then, I did the 2.0T coil upgrade and my misfire problems are long gone.

I myself am a mechanic, most my friends are mechanics, and I've spoke with coworkers whom have well over 25 years experience. They all agree that the smoke does not smell like coolant or oil.
One mechanic said after he installed a very expensive set of Hooker Headers on his fox body, that they smoked for about a week. Another mechanic suggested that since we don't know how long the previous owner drove around with the car misfiring/with a clogged cat, that it is possible there's a bunch of carbon build up just burning off. It does just smell like "new header/hot exhaust"

The down-pipe is just a cheap ebay down-pipe, so for the first 50 miles I suspected that they probably just put some really cheap coating on it and it would go away eventually. It's been idling for over an hour in my driveway, I'm looking at it through my window as I type this, and it's still smoking.

One last interesting piece, the other day, it stopped smoking. I drove it for maybe 10 miles with nothing. Then it came back as if it had never went away.

2003 Audi A4 1.8T Quattro with 256k
mods: 2.0T Coils, silicone TIP, 710n DV, DEI wrapped down-pipe, SAI delete, currently without a N249 valve (just got new one in the mail today, not installed) have been driving with a vacuum line straight from the manifold to the DV.