New non-retina 13.3" mac, will I get OS registered in the app store? I'm thinking of buying a 13.3" MacBook Pro that a store has at low prices right now.

Will this come with the OS registered in the app store? I ask because I plan to switch out the disk for an SSD, and with my previous MacBook Pro I could simply input my App Store credentials during boot and it would download and install everything directly.

Can I do this with a new MacBook Pro, or will I have to buy a separate copy in the app store to get this function?
The first time you start up the system and log into the OS, you'll be prompted to create an Apple ID or connect to an existing one. That will register the OS as 'purchased' and enable you to do Internet Recovery or download the OS from the App Store.

If you're using a MacBook with the same OS as currently available on the new MBP you wish to buy, it may be possible to simply take the SSD out of your existing MacBook and plug it straight into the Pro. (This has worked with me in the past with taking an SSD out of a MacBook2,1 and putting it into a MacBook4,1.) 

As for having to purchase the OS again, Mavericks is free. Any app that you've purchased/downloaded from the App Store can be installed on new systems free of charge.