If a person did not form the intention of fasting from the night before, can he observe a voluntary fast that day?

Sunan an-Nasa'i · Book 22 · Hadith 2321

أَخْبَرَنَا مُحَمَّدُ بْنُ الْمُثَنَّى، قَالَ حَدَّثَنَا يَحْيَى، عَنْ يَزِيدَ، قَالَ حَدَّثَنَا سَلَمَةُ، أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم قَالَ لِرَجُلٍ ‏"‏ أَذِّنْ - يَوْمَ عَاشُورَاءَ - مَنْ كَانَ أَكَلَ فَلْيُتِمَّ بَقِيَّةَ يَوْمِهِ وَمَنْ لَمْ يَكُنْ أَكَلَ فَلْيَصُمْ ‏"‏ ‏.‏

It was narrated that Yazid said: "Salamah told us that the Messenger of Allah (ﷺ) said to a man: 'Announce the day of Ashura. Whoever has eaten let him not eat for the rest of the day, and whoever has not eaten, let him…