Only if you have group write back enabled:
https://learn.microsoft.com/en-us/azure/active-directory/hybrid/how-to-connect-group-writeback-v2
https://learn.microsoft.com/en-us/azure/active-directory/enterprise-users/groups-write-back-portal
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In an Exchange hybrid environment 60% of mailbox are migrated to 365. All the distribution list are on prem. I try to "migrate" the dl on cloud by this steps:
On prem I extract the members and copy the X500 address.
Delete the dl.
Sync by ad connect to 365
Create a new dl with the same email address, add the members and copy the X500 address.
If I try to send a email from on prem to migrated dl I receive an error "Remote Server returned '550 5.1.10 RESOLVER.ADR.RecipientNotFound; Recipient not found by SMTP address lookup'".
You should wait till all the mailboxes are in 365 and all message traffic is between the 365 mailboxes and the 365 groups.
Its failing from on-prem because the SMTP domain in on-prem Exchange is authoritative and doesnt know how to route to the group in 365 since that email address is no longer on-prem.