No problem
I'm not sure on that... In my case, adding the CC was the process to get verified. (and I didn't send over $2000 -ot even close)
I'm not up to date on the limit you can send if you're unverified, at some point it was $700 I believe (or maybe that was for foreign accounts only)
Getting verified is a relatively easy process, and it involves either a CC or a banking account (they deposit 2 ridiculously low ammounts on your account and you have to enter those on your PayPal confirmation page or they charge you $1,95 on your CC and you have to type in the code that appears on your montly statement - also on your PayPal confirmation page)
Once you're verified, you can make payments using money you received from other people there, the CC or the bank account, (of course, you'd have to have the CC or the bank account on file to do it)
Since I don't have a US bank account, I only have my CC there, so I can just make CC and direct transfer payments.