Can Road Building Progress Card be played with only 1 road remaining?
Yes. There are no rules providing conditions that must be met to play development cards other than playing only 1 per turn, and not playing them the turn you buy them. So you would play the card, and then just do what you can to follow the instructions. If the instructions are impossible to follow, then you just do what you can. The same would go for playing a Year of Plenty if there's only 0 or 1 resource cards left in the resource piles.

I don't have a particular rule to quote for this, but it seems like the only logical way to handle it. The rules are clear about when you can and can't play development cards, and there's no mention of requirements of having enough roads left.