Installing CentOS 7 over Win7 in a dual-boot enviornment.
 

My machine is Ubuntu/Win7 dual-boot. I want to install CentOS7 over Win7.
If I pop the live CD in and boot up CentOS 7 and install it, will it give me an option to install on a certain partition?

yes

just do a custom install
and READ what is on the screen

Yes, the installer gives you the option to install on a specified partition.

No, that is not what you want to do.

You should delete the Windows partition and then either manually create partition(s) for Centos (and then tell the installer to use them) or tell the installer to use the unpartitioned space to automatically create partitions.

The partitioning tool you can get into within the Centos 7 installer has a strange UI and typically confuses people, even experienced Linux administrators. It isn't actually difficult to use and you can use it to do the entire job (delete Windows partitions, and manually or automatically create partitions for Centos all while preserving the Ubuntu partitions). But since you have Ubuntu installed and want to keep that as well, you may find it easier to use the GUI partitioning tool within Ubuntu to delete any partitions you want to get rid of, before using the Centos installer.