Are you wanting to run Conan adventures with DnD characters? Of course, a plot is a plot, and will transfer well, but the Conan adventures presume the players do not have magic items or buff spells, divination spells or healing magic. Your DnD characters will probably have those things, making the actual adventure as written too easy.
But if you use the plot and fill the NPC rolls with DnD characters, they should do alright. It would seem easier and less time consuming to create one's own adventure than to adapt one from one system to another.