Is craigslist part of the Shadow Economy? Many if not most of the purchases that take place there are done without taxation.
If we take the definition of shadow economy to be illicit economic activity existing alongside the traditional economy and further pin down illicit to mean any sort of economic activity that violates laws governing our conduct (civil, economic etc.) then the short answer is - yes.
Why? Many reasons. I think the easiest to verify and perhaps most obvious is that the majority of gigs, services, temporary labor positions, etc. on Craigslist are paid in cash. Here I make an assumption: most of the people doing these jobs for cash are not reporting these extra earnings. Thus, they are generating a supplemental income that goes untaxed.
I read a bit of (non-academic) research about how these sorts of sites often provide a lifeline to illegal immigrants precisely because they facilitate economic illicit activity (I will update this post with the link if I can dig it up).
Why else? Again I speculate (but reasonably). Craigslist, I think, is often used to move stolen property. Because transactions are largely anonymous and conducted on a cash basis and with little or no record of sale, CL is a safe place for petty criminals to liquidate stolen assets. This also clearly aligns with our given definition.
You could probably think of other reasons to support the claim that CL fuels (alternatively: is part of) the shadow economy in America. Then again, I think these two examples make it clear (if you are willing to accept the assumptions throughout the post).
Here, one of the examples listed is:
non-operation of the VAT system;
VAT being the Value Added Tax, such as a GST. When you buy a product on Craigslist, you typically would not pay GST on products you purchase here.
The straightforward answer is no, even if we use IZA's extremely broad definition of the shadow economy as any economic activity that goes unreported. Under the definition provided in 123's answer the answer is similarly no.
To understand why, we can look at Craigslist's business model, which comes down to classified advertisement. Craigslist is not a retailer. Since the revenue of said advertisement is neither illegal nor does it go unreported, it does not make sense to classify the organisation itself as part of the shadow economy.
Does craigslist facilitate the shadow economy? Most probably yes. You can, in fact, find an array of past cases of people being prosecuted for trying to offer illegal services on craigslist. But I would advice against the pure speculation with regards to the extend illegal services offered on the site.
Lastly: Would a removal of craigslist lead to a weakening of the shadow economy? That is certainly imaginable, but it is not clear that it would make a noticeable difference. Classified online advertisement is not exactly a monopoly market. Entry into this market is, in fact, incredibly easy.