No, reputation is mainly only tied to the IP address of the sending server. As long as a message is signed correctly and has proper SPF and DKIM entries in DNS, it shouldn’t affect spam detection.

I can’t say it won’t, because that’s really up to the receiving SMTP server, but industry practice is generally that the domain name is a very low value signal, compared to sending IP.

Brand new domains, as long as they’re being sent from an IP address with a good reputation, should have no issues.