Yes. For example your catalog and images could be on an external hard drive with the application remaining on a fast internal drive.
Taking Jon's reply a little further, the catalog and images can be on any internal or external drive, and they do not need to be on the same drive.
A common configuration is to have the LR catalog on an internal drive and all the images on one or more external drives. To edit images on external drives without the drive(s) being connected, you first have to create "smart previews".
Thanks for the reply! I think I will try lightroom and maybe get thousands of photos organized.