Not quite. It's actually:

In the US:
- server brings bill to table
- customer puts credit card in the bill
- server takes credit card to machine and runs it for total amount due without tip
- server brings back credit card and credit card receipt to table
- customer fills out tip line and signs
- at some point after the customer leaves, server takes bill back to machine and enters total with tip for final processing

In most cases, the server won't know the amount the customer tipped until after the customer has left the restaurant. I have had servers ask if it's OK to take the signed receipt before the party has left if the party is lollygagging at the table and the server is about to go off-shift (or the restaurant is closing), as they need to settle their transactions before they can leave. In these cases, the server will see the tip line with the customer still present, but it's fairly rare.