The configure button is not available if you are not running at least Exchange Server 2013 SP1.  I have installed Exchange Server 2013 CU7 on both of my Exchange 2013 servers.  Is CU7 considered a "higher" release than SP1?  If so, will the Configure Button be available to me in the Hybrid Configuration Wizard or will I need to manually configure the OAuth authentication between my On-Prem and Exchange Online organizations?

The configure button is not available if you are not running at least Exchange Server 2013 SP1.  I have installed Exchange Server 2013 CU7 on both of my Exchange 2013 servers.  Is CU7 considered a "higher" release than SP1?  If so, will the Configure Button be available to me in the Hybrid Configuration Wizard or will I need to manually configure the OAuth authentication between my On-Prem and Exchange Online organizations?

Yes CU7 is the latest release. SP1 was CU4.

A far as OAuth:

https://technet.microsoft.com/en-us/library/hh529921(v=exchg.150).aspx

The wizard checks to see if there is an existing OAuth authentication relationship or a federation trust with the Azure Active Directory authentication system for the on-premises organization. If present, existing OAuth authentication or the federation trust is used to support the hybrid deployment. If not present, the wizard configures OAuth authentication or creates a federation trust for the on-premises organization with the Azure AD authentication system, depending on the type of on-premises Exchange configuration. The wizard also adds any domains selected within the Hybrid Configuration wizard to the federation trust if needed.

In addition to the OAuth authentication or federation trust configuration, the wizard also creates and configures organizational relationships for both the on-premises and Exchange Online organizations. These organization relationships allow the wizard to enable several hybrid deployment features, including free/busy sharing, Outlook Web App redirection, and MailTips.

Hi,

If your on-premises organization is running only Exchange 2013 servers with Cumulative Update 5 or later installed, run the Hybrid Deployment Wizard instead of performing the steps in Configure OAuth authentication between Exchange and Exchange Online organizations, for your reference:
https://technet.microsoft.com/en-us/library/dn594521%28v=exchg.150%29.aspx?f=255&MSPPError=-2147217396
 
Best Regards,
Allen Wang