Almost certainly not. Some people have tried and had success. I've always had issues, and sometimes found that even when it worked, it resulted in stability or performance issues down the track. You could try, but I personally wouldn't recommend it.
The good news is that what you're describing probably counts as a "significant hardware change" under Microsoft's Licensing agreement, which means you can use your current Win10 Pro license and don't need to buy a new one.
This is all legal and fully legit - straight from Microsoft.
You can follow the steps here:
https://support.microsoft.com/en-au/help/20530/windows-10-reactivating-after-hardware-change
To link your current license with a Microsoft Account.
Then download a fresh Win10 Pro copy here:
https://www.microsoft.com/en-au/software-download/windows10
(Make sure you get the right version (32/64bit - Home/Pro - otherwise it won't activate).
When you install it fresh on the SSD you just "skip" putting the license key in. But then follow the instructions on the bottom of the Activation guide I linked above to re-assocaite that Win10 Pro license with your updated build.
Still involves a fresh install, but at least you don't have to buy Win 10 again.
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