Given that the original is still activated there is no reason they couldn't both remain activated - the original is activated via the BIOS provided details & the SSD would be activated by the printed key.
Just a thought - I think the ISO you download from MS is generic and not specific to the key provided. Not sure about the pro/home side of things though. If you can find someone with the required version installed they could download an ISO for you.
And another - have you tried creating recovery media using the laptop?
VAIO User Guide | Creating Recovery Media