Yes, many medieval (post-Christianisation) texts in Scandinavia were still written in runes rather than Latin alphabet. Unlike Latin, Runic texts and inscriptions seem to be primarily used for mundane, common communication, whereas Latin (including the script) is tied to the Church and official stuff. The Novgorod birch bark letters are a good example of the use of runes for common, everyday communication on perishable material during the Viking age. One would not waste expensive parchment or paper on that, but the same is true for Latin. It is entirely plausible that formal communication during the Viking Age would also have taken place in runes, on parchment. I do not know of any pre-Christian Runic books though, these are all Medieval.