We currently have an SCCM 2007 R2 environment which is 1 primary site.

In AD, we have 1 forest with 1 domain and 1 (AD) site.  We are now going to add a new AD site for a child domain. At this time, we are not going to add a second SCCM site.

Within the SCCM boundaries, there are IP subnets defined for client workstations.  In addition, there is the "Default-First-Site-Name".

All boundaries are designated as fast connections.  None of the boundaries are protected.

Since there is going to be a second site added, I would like to delete the Default-First-Site-Name boundary.

I am thinking that I will just need to add in the applicable IP subnets (or preferably IP address ranges) for the remaining subnets I want to discover in both AD sites?

If the new site and subnets are added to AD prior to changes being made in SCCM, will discovery for the Default-First-Site-Name be impacted? (IE, does the Default-First-Site-Name boundary discover any object that is not defined by the IP subnets we have defined)....

Site boundaries and discovery completely 2 different things.To discover computers into SCCM from AD,you dont need boundaries but to manage the computers,you must define boundaries which can be AD site,Subnet,IP address ranges etc. Discovering resources from AD doesn't mean,they are managed but should have boundaries defined before you manage them.

Coming to the problem,since you only have 1 primary ,you can add the newly created AD site boundaries into SCCM either IP subnet,IP address range . I am not clear with your question what you asked.

Boundaries are nothing to do with Discovering resources from AD ,but to manage,you need boundaries. You can add multiple boundaries could be AD site,IP address range,IP Subnet since you only have 1 primary site .

Jason wrote nice blog post explaining about Site Boundaries ,can help you to understanding (Additional info)  http://blog.configmgrftw.com/ip-subnet-boundaries-are-evil/