Is a home pregnancy test accurate 32 days after unprotected sex?

No reason not: Double negative, should be positive. So, I'm thinking you've not had a period since the unprotected sex. If the test results say pregnant - it is probably true and a doctor can confirm it and begin pre-natal planning or consult about other options if they are of interest. If the test is negative, a visit to the doctor might find the cause of a missed period and offer birth control info/Rx. Best!