Should I expect any implications due to specifying credentials explicitly rather than selecting service account option?
There should be no issues specifying the credentials explicitly.
Also are there any options to control when warning messages should appear for specific actions in Adaxes? Because for brand new mailbox there will be no corrupted/oversize items so warnings are not needed:
The warning in your screenshot is generated by Exchange Online. Adaxes writes all execution warnings to the execution log. This behavior is by design and can’t be disabled.
As far as we understood, you are creating new users with mailboxes and moving the mailboxes to Exchange Online after creating them. In this case, you don’t have to move mailboxes. Mailboxes are created in Exchange Online when the appropriate Office 365 license is assigned to the users.
If Exchange is in hybrid mode, Adaxes automatically enables and disables remote mailboxes when assigning and revoking Office 365 licenses with Exchange Online. You can configure how Adaxes enables or disables remote mailboxes. For details, have a look at the following help article: https://www.adaxes.com/help/?HowDoI.Per ... boxes.html.