Technically yes, you could - but I'd not recommend it.
Windows will automatically install new drivers to match the hardware of the new machine (because if it doesn't, you'll probably find it barely functions). That can be problematic in itself, though: some hardware in the new machine may not work properly, which may leave you manually reinstalling drivers and trying to disable no-longer-needed drivers that Windows didn't correctly handle. Further, you're likely to have the same problem when you later put the drive back, by which point you'll have doubly messed up your machine.
If it's data that you want to keep hold of, I'd suggest buying a USB drive caddy so you can plug your SSD in to another machine and access your data. If it's the OS, apps and settings you're worried about, and you really don't want to take the machine, you could leave it on and connected somewhere where you can access it remotely (e.g. use Teamviewer, VNC, RDP over the internet from another machine).