Not deliberately, but I inadvertently do it reasonably often when I have samples I'm analysing by NP and RP.
It usually doesn't work in highly-aqueous mobile phases. The components that are soluble in hexane drop out in RP solvents, blocking guards, and the peaks that do appear are seriously deformed, telling me that I messed up.
If the hexane doesn't dissolve, you have a slow flush with a miscible solvent ahead of you to clean the system. I keep getting reminded that methanol, water, and acetonitrile aren't miscible with n-hexane.
I've never encountered a situation where samples in an immiscible NP solvent gave superior peak shape on RP columns to samples in RP solvents.
Some solvents that are miscible in bothe phases, eg IPA, work OK, but I still like to match the sample solvent to the mobile phase, as that means insoluble material usually remains in the sample vial.
Please keep having fun,
Bruce Hamilton