Can blacklisted IPs affect my email service?

If a IP address is blacklisted, it has no impact on your email service whatsoever.

Your email service uses your origin server’s IP. You can take a look at the mail delivery SPF records to verify this. They should look something like v=spf1 a mx ip4:123.456.789.123 ~all. The numbers listed after ip4 will be your origin server’s IP address, and not a IP.

The only IP address that affects your mail delivery is your origin server’s IP address.