Of course it is possible. Although you need to freshly install Mac OS X on it.
When that is done, you can boot from it.
BUT back up your 1TB hard drive first (time machine will do).
Now, when it comes to you personal data, you need to transfer the applications over to the SSD. The best option for that is to reassign the applications folder.
There are guides on the internet explaining how-to. The end result will be that the application folder on the 1TB Drive will have the icon of being a home folder.
You can do the same stuff for all the other stuff you'd like on that SSD. Eventually move it all to the SSD. Then erase it and put all the files back on it, so the system files and all are gone.
You can, with a little help of migration assistant, transfer all your personal settings over the new SSD.
This may sound difficult bit it's quite easy to be honest. But YES, it can be done.