My Acer laptop came with Windows 10 pre-installed, but it was an earlier build, I'm not sure if a recovery disc will resolve that issue, since I've never had to use one, I do still have both my old Windows 7 Home Premium discs (32 Bit and 64 Bit), so I was able to use the serial that came with them, when I did the upgrade to Windows 10 on my studio desktop pc.
I've actually found it easiest to just do a google search for the latest Windows 10 installer Iso file from Microsoft's website, and just do a complete backup/re-format/clean-install every 6 months or so.
As far as I understand, when you do the upgrade from Windows 7, or 8, to Windows 10, the serial that was linked to the computers running those versions of Windows, and stored on Microsoft's servers, is used to activate Windows 10 on those devices, I may be wrong though, but as long as Windows 7 and 8 were properly activated on those computers, you shouldn't have any problems, Microsoft offered Windows 10 as a free upgrade for Windows 7 and 8 when it was first released, I took advantage of the offer as soon as I could, haven't had very many problems with activations so far....touchwood.