Yes. I have multiple systems spread across a couple of SSDs.
I relocated a number of these encrypted systems to a new SSD recently, and cloned a system too. Re-installing is not necessary at all.
The same process should allow you to clone your existing system to a different partition and file system.
This is not a cut and paste tutorial, read it and understand how it would apply to your situation.
If your system is not encrypted then just obviously ignore the cryptsetup bits.
You must ensure your new btrfs partition is correctly configured and mounted before rsyncing your ext4 system to it.
Will you have a separate efi partition for you system? If so create it with the appropriate flags before chrooting and installing grub.
If you are unsure probably best to do a couple of test runs in Virtualbox, to iron out any kinks before going bare metal.
NOTE : This applies to cloning a system on the same physical machine, where drivers and driver config would the same. Cloning a system to a different physical machine is probably more trouble than its worth.