Yes, it's possible.
Rather than Time Machine, clone the drive in the MBP with Carbon Copy Cloner or SuperDuper (you have to pay to get scheduling with SuperDuper, but manual cloning is available with the free download).
Boot to the new drive first to check that it works, then all you have to do is swap the drives.
I did that before I changed my iMac hard drive.
You'll need a laptop drive enclosure or something like
this adapter.