Yes you should seal your handle.
All wood swells up when it gets wet - a phenomenon called wood movement. It's why doors and gates occasionally jam during winter due to water being absorbed from the surrounding damp atmosphere.
If your handle scales swell up too much from either sweat or atmospheric moisture/ humidity, it can potentially affect the throw angle of your blade, especially if it's on the flexy side anyway. Most fine line handles have the wood grain oriented to avoid excessive swelling, but it differs from blade to blade.
Sweat / sebum / dead skin cells do NOT effectively seal timber. This sort of debris is not very hydrophobic compared to regular methods (nor it is very sanitary!) For skin debris and sweat to effectively seal a blade, your sebum would need to effectively act as a drying oil, which it simply doesn't. It simply doesn't cure properly. It also becomes a potential vector for yeast, fungal, and bacterial growth, so just seriously... Ew! Yuck.
Sealing your handle helps prolong the life of your blade. If you sweat excessively from your hands, water from your sweat will start to permeate the core and outer layers of your blade via the open end grain at the bottom of your handle, and will permeate your blade's medial layers via the open end grain on the handle sides itself. Moisture can then 'wick' through the wood's fibrous vessels and surrounding tissue like water up the stem of a cut flower, causing the wood to start to swell and degrade, which effectively means bye-bye blade. If your blade is made with water soluble type one PVA, this will also soften the glue lines over time, hastening the process.
Sealing your blades properly isn't difficult. Traditional drying oil like tung or linseed oils will do the job. if you also use a little 240-400 grit sand paper to LIGHTLY rub down the handle while the oil is still wet, this will also help seal the pores in your handle scale, (assuming that is they used a hardwood to make the handle scales.... This is a traditional French polishing technique, but it does not work so well with softwood handle scales, as they don't have any pores to begin with. If the artificial wood dyes in your fine line handle are also oil based (unlikely but still possible) this might also cause them to run a little bit)
Myself I use Osmo oil to seal my handles. It's a hard wearing, natural blend of plant based drying oils and natural waxes such as beeswax and canuba wax. It's available world wide, and does a magnificent job. It also does a fantastic job of deeping and highlighting the wood grain (assuming that is your handle has decent quality natural wood in the handle, and not the typical heavily-dyed cheap-arse fine line handles most manufacturers use.)
If you can't find Osmo oil, or don't want to pay it's high purchase price, you can try regular danish oil, or bees wax, or candle (paraffin) wax, or even regular polyurethane if you absolutely must.
Alternately, you could simply try burnishing the handle of you like, by simply rubbing it vigorously with a rough cloth, metal scraper, or the back of a piece of sandpaper. If any of the wood's natural oils and extractives are left in the wood after the fine line manufacturing process (which I doubt) they should blend with the melting lignin and form a seal on the wood (assuming there's still enough lignin left in the handle scales as well. Don't try this trick with your playing surface though. The problem with burnishing some woods is any low density areas in the surface can result in corrugations and/or low spots on the playing surface after burnishing... This is not quite such a big deal however with the handle, as it's perfect flatness doesn't matter as much).
But please, for the sake of your blade and your health, don't rely on old sweat, dead skin cells and stale aging sebum to try and seal your handle... No disrespect intended to the original poster, but not only is that a pervasive myth, it's also the most genuinely unhygienic and stomach-churning suggestion I've read in quite a while.
