I guess that really depends on what you mean by, 'it should not matter if the "full" Windows Defender app is used or not.'
It certainly would. That URL database in all likelihood does not even exist for the pre-Windows 8 implementation of Windows Defender and in the Windows 8 and later implementation would still require that Windows Defender definitions (which would include said database) were being updated on a regular basis.
The Windows 10 (and I'd presume 8, but I don't have it to check) version of Windows Defender can now be run without realtime scanning as a secondary checking mechanism side-by-side with most of the major 3rd party antivirus/security suites. It would have to be doing so, at a minimum in that mode, for the URL database to be kept up to date.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1803, Build 17134
Memory is a crazy woman that hoards rags and throws away food.
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