Can I apply Arm-R-Seal over green mesquite wood?

Green mesquite is too oily to accept General Finishes ARM-R-SEAL - it will not dry properly.

Mesquite is resistant to most oil finishes, but it easily accepts shellac, oils, and waxes. We recommend shellac instead because it doesn't react to the oils in the wood. Here is a good resource to find about: properties of various wood species.