PVA's and aliphatic resin glues need porous surfaces for a good bond. It may stick, but not well at all or for any length of time, and have very little strength. So, for a short answer...no.
I agree with cabinetman that it won't work. You could use a paint and varnish remover and strip the danish oil off. Another option is you could mill the wood out and insert an oversize spline. That way little of the wood with the danish oil would be glued.
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