They won't have to investigate when they have a 1099-K from eBay and bill you for tax.
But it doesn't matter. Listen to our advice or not, it's your problem.
It's as simple as this ^^^^
I'm going to use easy numbers. Let's pretend you have a regular job and make $30,000/year. You file your taxes and don't include the other $20,000 of gross sales (i.e. payments received) via PayPal (again we're assuming you took in exactly $20,000 in online sales---doesn't have to be just eBay but any payment you received into your PayPal account).
The IRS is still going to get a 1099-K from PayPal on your behalf. They will see that you filed your taxes for the $30,000/year you make during your day job and they will also conclude that you have another $20,000 of unclaimed income that you failed to file.
This requires very little to almost no resources on the IRS behalf. The computer will flag that you didn't report earnings and someone will take 15 minute to review your file and realize that you didn't report your 1099-K.
Their initial stance will be that all payments received are pure income since you didn't file any business expenses. They will send you a bill for the taxes that you would be expected to pay on an additional $20,000/year based on your income. They will also asses underpayment penalties.
It will then be your job to prove that not all of the $20,000 was income. Have fun with that after that.
If you file correctly from the begginning and fudge numbers in your favor then yes, it is very likely they will NOT catch on. If you fail to file altogether it is very easy for them to catch that since your reported income won't match what they recieve from your employer + paypal (i.e. W2 + 1099K would = total income if you have a day job and sell online on the side).
Bottom line is that your income from job A + 1099-K must match, so intially you must report the $30,000 + $20,000 = $50,000 as your income and the deduct item costs, and any other business related costs. If you can effectively do that to get your actual income back down close to the $30,000 range then good for you.
As someone else mentioned I thought a 1099K was only generated if you met both qualifications:
1) 200+ sales in a calendar year
2) $20,000 in gross payments received in a calendar year (again we're NOT talking profit here)
If you didn't meet both then I'm not sure why PayPal would need you information other then it wouldn't surprise me if they are requiring all account holders to have a SSN on file and may be hounding those who created accounts when that wasn't a requirement