Yes, they were.
The Prophet chose the scibes and under his supervision they would copy word for word. Known scribes were: Ali ibn Abi Talib, Abdullah b. Masud, Abu Dardah, Zayd b. Thabit, Ma'adh b. Jabal and Salim Mawla Abi Hudayfah.
Ibn Nedeem (Al-Fihrist, p. 41) recorded 41 companions who had written the entire Qur'an with their own hands during the lifetime of the prophet.
In the Holy Qur'an there are many Verses which talk about the Qur'an as a book.
It is (recorded) in those scripts (of the Preserved Tablet) that are
honoured, exalted, purified, in the hands of those scribes who are
honorable, righteous. (80:13-16)
And they said, .(These are) the tales of the ancients he (the
messenger) has caused to be written, and they are read out to him at
morning and evening.(25:5)
Additionally , the famous hadith of the Prophet, about the two weighty things he would leave behind, says:"I leave among you two valuable things, the book of Allah and my progeny".
The word `book' denotes existence of a collection and not of scattered
scribbles, nor of things which are in the memory but not written.