Hi,
Yes, you can connect to Exchange Online powershell using administrator permission.
Use the below command to provide folder access
Add-MailboxFolderPermission -Identity ******@contoso.com:\Draft -User ******@contoso.com -AccessRights Owner
Refer for access rights https://learn.microsoft.com/en-us/powershell/module/exchange/add-mailboxfolderpermission?view=exchange-ps
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