I was foolish enough trying exactly that on a whim around 10 years ago, and it worked great actually.
Not the same wood, this was on hard ash and I also did let the grain raise (water based paints will do that) and didn't sand it down before the "oil" application for an additional effect.
Just after the first oil coat, still wet:
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Few more coats and lightly sanded down with steel wool
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Cool. So that works too.
Nice finish. And great grain pattern on that!