Hello! Is Windows Small Business Server 2008 compatible with the new Windows 10 on adding a computer to the network? 

Thanks,

Rob

Hi

 Windows 10 compatible with these OS,(client connector availability)

Windows Home Server 2011
Small Business Server 2011 Essentials
Small Business Server 2011 Standard / Premium
Windows Server Essentials 2012
Windows Server Essentials 2012 R2
Windows Server 2012 R2 Standard/Datacenter with Essentials Experience Role

Also you can detailed information on this article

http://blogs.technet.com/b/sbs/archive/2015/07/23/client-connector-availability-with-windows-home-server-small-business-server-and-windows-server-essentials-for-supported-client-os.aspx

• Edited by Burak Uur 16 hours 0 minutes ago

If you mean to simply add the computer account to the domain, you should had no problem to do so

Like told there (https://social.technet.microsoft.com/Forums/windowsserver/en-US/a654c16c-2d4d-483a-b840-60d16975050b/windows-10-and-a-server-2008-functional-level-domain?forum=winserverDS)