All in the title.

My potential new player has sent me his starting build.

Hes taken a Vibrosword, with a Mono-Molecular Edge, and a Stun Pulse.

Is this allowed?

Should I allow it?

He will be joining a group, and getting 180xp to bring him to to the same levels.

Nothing against Attachment buying as long as they've got the credits and it's not Restricted (at which point you, the GM, have to okay it first). Usually there's no real problem, and it generally makes sense to have the attachment already attached to the weapon/gear, but if you really wanted to, you could potentially have him spend in-game downtime to apply the attachments first.

Weapon attachments are fine, but mods require a mechanics check. I still required a mechanics roll from my players who want to mod their attachments at character creation.

Yes to attachments, but the mods should (IMO) be made in the context of the game, since they do require Mechanics checks.

I would have a PC make those Mechanics checks in the opening scene of the game. I usually start things en media res... so for the player who wanted to start with modded equipment, I'd probably just include his Mechanics skill checks in the beginning narrative, probably as one scene in a montage that focuses on each of the PCs (or possibly as separate groups), and then have each of the others perform some other skill check as appropriate to the scene(s) at hand.

How does he install the Stun Pulse in the vibrosword? I mean it's technically a mod for bludgeoning weapons, but maybe he plans to install it in the pommel? (You could houserule the pommel counts as an improvised weapon.)