I need to move one SMTP domain between Office 365 tenants. If I add this domain to tenant 2 so that I can get the TXT record for for verification will it have effect for email routing for users that are sending mail to this domain from tenant 2?
You have to follow this process.
You can use Cloudiway's tool if you need to migrate from one Office 365 tenant to another.
Check it out https://cloudiway.com/solutions/migration-between-office-365-tenants/
Domain migration between tenants is not possible with the manual method, but you can perform this task. To perform this task you have to take the help of automated solution in which you can migrate a domain users mailboxes between tenants. Visit here - https://www.systoolsgroup.com/updates/how-to-move-domain-between-office-365-tenants-migration-guide/ to get all steps to perform this task.