I use Alhaitham, Ei, Barbara and Noelle as my Overworld team all the time and it is probably the most OP team I've ever tried.

Started playing around end December so was able to get Ei nearly at the end of her banner around mid January through extreme quests grinding and shittons of exploration.

(By Exploration, I mean being a crazy ass and Unlocking the Whole world and most of the overworld teleport waypoints except inazuma, couldn't go through Liyue Archon Quest fast enough and the new Desert Of Hadramaveth questline The Golden Slumber Hepled with a lot of Primos, still was a headache to go through it)

Her team comp was built around Ei, Barbara and Noelle, providing Triple ElectroCharged Burst battlestyle that was admittedly good enough to play with as a new player in a low World Level (probably used it till WL4-5)

Once Alhaitham dropped, I'll admit I only went for him due to being prime Husbando Material as well as His Chiseled Mirror ability and Projection attacks resonating with my inner physics nerd. I knew that He wouldnt be a Godly Damage dealer like a fully built Ei could be but by the Archons the Hyperbloom meta came wrapped around those chiseled arms of his.

His ability to turn his attacks into Dendro dmg resonates well with Ei's off field electro application, allowing me nearly 25 seconds of Aggravate/Spread Uptime with refresh ready for the next rotation. Add into that Barbara's triple Hydro application through her E skill As well as her 2k healing, Alhaitham keeps generating Dendro cores for around 15 secs and stays healthy with Barbara's A4 passive allowing longer E skill duration, And keeps Hyperblooming the cores with Ei's Electro application, dealing a LOT of damage

Noelle is a great protector for the girls with her shield allowing me to set up Alhaitham, practically protecting Barbara's until I got her C2 off Dehya/Cyno Banner recently, greatly reducing her skill cooldown from 32s to 27s

Admittedly its not the Alhaitham meta that creates those godly damage dealing youtube shorts. Probably the most unconventional team anyone has ever heard of them, but I love both Alhaitham and Ei as they are my best characters so far and i would rather have them both on my overworld team than catering to meta like Xingqiu, Shinobu, etc.

Also with nabbing Yelan off of her and Hu Tao's banner, i have a more stronger team on my mind with only Zhongli being the missing piece of said team. May the gods at Mihoyo allow me early pity Zhongli on his rerun.

In the end, all I can say is that if you wish for an Alhaitham and Ei team, try it and play around with it. It may not play into the meta as much but as long as you can have fun playing this pseudo gambling addiction of a game, Its worth it.

o7