Shareena and alfonse

I already had Sharena as a fully built five star and Alfonse as a mostly built four star so it was pretty easy for me. And while they definitely aren't as strong as some of the other units in the game, they're totally worth investing in. The 3 starting units are always in quests and bonus in the arena so they're overall just very useful to have, even if you don't plan on using them regularly.

I think you can actually do the quests without going to the BhB! You can just defeat them in a story chapter and it still counts.
Don´t know which chapter they appear in but I think I´ve read it on their BhB page

They are the starts. they are always coming up for quests and are a free bonus unit (with legendary weapon) every arena season.
It's totally worth upgrading them to 5*, upgrading them to 4 star is a nobrainer really, go for it.

My question then is, is it worth it to give Alphonso his legendary weapon for the points, or can his BRave Sword do well ebough on scoring?

You can do this with the 3* version.

Also if you notice Alm or Celica in the Tempest trials just surrender your current team and sub in Alfonse or Sharena to kill them. It will affect your score on that run but who cares, an orb is worth it.