score:3
The short answer is "no". You should be able to check-in and fly without any issue. No for the invoice, you might not receive it if the address is wrong. You can probably contact the airline to make the correction after the fact.
Upvote:2
Billing address is strictly for billing. If they issued the ticket, you are fine.
For most vendors, the credit-card company gives them progressively lower rates as they collect more information, so if the vendor supplies your name and address, the transaction only costs them (for example) 1.8% but with the credit-card number, it's 1.9%.
Once you have the ticket, only your name (and, if they are feeling enthusiastic, your birthday) matters.
Upvote:2
You should be fine. Generally the credit card is at least authorized at the time that you check out, so if the system required an exact match on the billing address it would have flagged as an error at that point in time.
If you want to double check you could always check your credit card account to see if the payment has gone through.