I have a 13" MBP and just got a new 500gb HD to pop in replacing my 160gb one. I have about 200gb free on an NTFS external I was planning on using time machine to back up my system for seamless HD swap but as we know, macs don't play nice with NTFS. If possible, I would like to not have to re-install all my applications and such. I found other software (SuperDuper) that should do the same thing but none will play with my NTFS external. I guess my question is this:
I have a SATA to USB adapter, can I:
Plug in new HD via USB, Format to OSX Journaled, then do a time-machine backup to the new drive, pop in the new HD and be good to go?

Of course not, a drive with a Time Machine backup on it is used to backup to another drive, it is not a bootable drive itself.

Do what the other poster said, use CCC to clone your whole drive to the new drive before you install it, and use the same name for the HD too (probably not essential, but it can't hurt, and you can change the HD name after it is installed anyway if you need to).

You should be aware that there are cases where user installed drives are problematic, it really varies from drive to drive and from computer to computer, and there are several work-arounds, Mroogle it or see
https://forums.macrumors.com/threads/729883/.
The HDAPM thread on the Apple forums has a link to the latest version too, and several people say it works well.
Not everyone is hit by this issue, I have no trouble with the Seagate in my MacBook Pro 15" but I did have problems with a WD 500GB 5,400 rpm drive.
Also, be very careful not to lose any of the screws when you take off the back panel, some are very small! And some go back in at an angle, so use you Apple manual that came with the machine for reference.
Good luck.