To my understanding, Rosewood and Ebony (which are the most commonly used fretboard materials in acoustic instruments) both retain natural oils. This is why there is no need to finish these woods with lacquer or other types of sealer. Maple, which is a very popular choice in electric guitar fretboards… especially Fender telecasters and stratocasters, needs to be sealed (usually with Lacquer or urethane).
So to answer your question yes, it’s good to oil your fretboard occasionally. Sometimes the natural oils in Rosewood and Ebony can somewhat dry out and a little extra help is good for the fretboard… and it just looks nice! But first, clean the fretboard. Any household cleaner will work. I use an old toothbrush to get into the grain and get next to the frets. Then wipe it all dry and apply your oil. Lemon oil seems to be the preferred choice for fretboards (that’s what I use). Only use the oil on the fretboard. Use a polish for the rest of the guitar. Two or three times a year should be plenty which is about how often I change my strings. More often won’t hurt anything at all IMO!
Keep in mind, this is only my opinion and others may feel differently and hopefully will chime in…
Great topic and not very often discussed… (should be)!