I've stained the maple neck of my current build to make it match the theme better. You can see some of the stain on the frets that I'll clean off with a dress when it's done. The fingerboard is satin poly finish here.
There is no reason not to - it's not going to change the properties of the wood or anything. You can then oil, seal, clear over it you want. My last TL build I did the maple fingerboard in poly to stop it going grubby. I really like the way it feels and plays, all my other guitars are oiled rosewood and it isn't any better or worse than those IMO.
I actually think the maple with the darker butterscotch body looks good - but everyone has their own taste so you do you
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