Google’s John Mueller said that using a different domain name for your web site and your company email has no impact on your SEO. In fact, I believe those who work at Yahoo do not use Yahoo.com emails but rather yahoo-inc.com emails, or at least they use to.
It is actually not that uncommon for large companies to use different corporate email domains than their website or website domains.
This topic came up on Reddit where the person asked, “Curious if the use of the domain email is a ranking factor at all? I ask because I try to rank one domain, while we use the email of our business name.”
John Mueller from Google replied in the thread saying, “why would it be?”
I mean, I am sure there are a ton of you that manage websites or own websites where you don’t use email accounts on that domain. You might have some support-related emails redirect to your current email but that is it.
Again, Google Search does not care if you use email addresses on that domain or use a different domain name for your email.
Forum discussion at Reddit.