Seeing how Warcraft III was released after 2000 and has always been playable in a HD resolution, this term makes no sense.
A more correct term for it would be Classic graphics.
The new reforged campaign will almost certainly not be available with classic graphics. It is designed for Reforged graphics and there is no reason to design it to support classic graphics. The only people able to play it are those who have brought Reforged and so have access to Reforged graphics.
Yes it is a Reforged feature.
The classic campaign will likely be used when running classic graphics. This way people without Reforged can play the classic campaign as they currently can and people with Reforged can play the Reforged campaign.
Another possible implementation would be to add 3 campaign selections, one for RoC, TFT and then Reforged. This would keep the implementation most true to the original without any of the nonsense of having to change game versions.
If it can be played with Reforged graphics enabled then it will partially support them. However only maps which were modified to be part of the Reforged campaign and are being played as part of the Reforged campaign will fully support the graphics. Partial support means that some assets which were not given Reforged graphic versions may still use their classic graphic versions and so appear out of place.
That said for the most authentic experience it would be best if they only allow the classic campaign with classic graphics and the Reforged campaign with Reforged graphics. This avoids any potential visual bugs due to missing or changed assets.