Many credit card issuer banks (“Issuers”) will decline the transaction if the billing address is entered and it’s wrong.
IME, 90% of online Merchants don’t bother to ask you to enter your credit card billing address. That’s because (1) the card network doesn’t ask for it as a mandatory piece of information to process the payment (2) it’s an additional friction hotspot that could cause abandonment and lost sales.
But the 10% of online Merchants that do ask you to enter your credit card billing address despite #1 and #2 above do it probably because they’re extra cautious about fraud.
UPDATE DATED 2 APR 2019:
TIL that a credit or debit card payment can go through even if you enter a wrong CVV. You gotta wonder how safe is Card on File. https://t.co/ia9gPDv3Ya via @stripe
— GTM360 (@GTM360) November 16, 2018
So, on second thoughts, I’m guessing that Issuers will indeed approve a transaction even if you enter a wrong billing address (but I could be wrong).
UPDATE DATED 4 SEPTEMBER 2020:
After a long, long time, I recently came across a Merchant who asked for my credit card billing address on its checkout page. The (prefilled) billing address was wrong. Still the transaction went through.