Is this sword worth of upgrading and socketing for a smiter pal?

I've found this sword, and it looks quite intriguing on paper, but I'm always confused at determining the actual damage output for a paladin-smiter.
My current hero sports this mid roll Grief Berserker Axe paired with an upgraded and socketed Herald Of Zakarum shield.
It literally takes under 2 minutes to clear Uber Tristram with that now level 86 smiter. I'm curious if it would be beneficial to upgrade the sword and place a Larzuk order for socketing. I can easily do all of that, but doing it and discovering it's been a major waste gives me a pause. Thoughts?

For Smite only FLAT dmg adds up as in Grief or for example Astreon's Iron Ward and Stone Crusher so I would say no it's not worth it. Grief is the only weapon that has massive +flat dmg bonus in comparison to others tho. Actual dmg from a weapon or any other sort of +max/min dmg or % to it doesn't work.

P.S. Before you dump it, what color is that sword in inventory screen?

Its a nice sword but it doesn't hold a flame to Grief - that flat damage just cannot be beat.

In an overly simplified expression:

Dmg= ((weap base dmg * %weap dmg) + flat dmg) * %offhand dmg
*then comes all the other dmg like Critical Strike, elemental dmg, etc, which I won't go into now since its not germane to the question*

Grief is so stupidly good because the flat damage is added together with the Holy Shield damage BEFORE all other sources of off hand damage. Now Grief is even godlier for a smiter because the flat damage is added before the Smite skill damage bonus:

Smite dmg = (Shield dmg + Holy Shield dmg + Grief/flat dmg) * (1 + (Smite ed + Str ed + Fanaticism ed + off-weapon ed)/100)

Thanks for prompt and to the point responses, greatly appreciated. However, I can't promise I wouldn't try bringing this sword to its full potential, lol. Blame darn curiosity. As to the color, it looks kinda greenish, akin to Bul-Kathos' Tribal Guardian, but much brighter.

That ED is around +30-50 damage, I would say , 35. and +2 skill, lets say it is 20%.
Make it up to 50.
Smite does not take your upgrade.
Still, it very far compare to Grief bottom 340.

As for socket, you can add Ber, 20%.
That will make it looks like something.

However, it is much weaker than Astreon's Iron Ward + 4 skill , socket Ber.

Smiter can equip Astreon's Iron Ward , socket Ber. And this weapon is kind of...rely on CB.
My recommendation is get a cheap one with DR 7, socket Ber. Dont spend too much on this. Put Grief as second weapon. When CB kill enough, swap it.

Still....easy and trivial way is just Grief kill all.

That kind of weapon is more zealer oriented than smiter.

As explained before, it will almost not boost your Smite damage.

You better have to compare your War Sword to Death Cleaver which is way better for a zealer.

As noted by others, Grief is just OP and hard to beat.

If you didn't have Grief, a regular Black in a Mace has 40% crushing blow so it would be better than this sword on a smiter.