Not really. I scan everything I get on paper, and put everything on Google Drive.
But it would be quite a lot of effort to dig through my hundreds (thousands?) of PDF documents that I have on that drive, and to find something that can actually be exploited and is worth more than what an attacker could get by just having access to my computer. An attacker can get my credit card numbers when I shop online, access to bank accounts when I am using online banking, get all my tax data when I file income taxes... I think that's far worse than anything that can be found on my Google Drive.
So I think having a separate laptop is overkill, unless you have something that's really more at risk than the data on the internet-connected computer.