I haven't used paypal for a while, but yes, you should be able to receive payments, but they will remain in your paypal account. If you want the actual physical currency, you need a linked bank account, then you can transfer money from the paypal account directly into your bank account if needed.
It's been a while since I set mine up, but I believe Hawkeye is correct. In addition to that, I believe linking a bank account is one of the steps to verifying your account. Without a verified account, it will put restrictions on your account.