Does a level 9+ Synthesist Summoner have Multiattack when fused with their eidolon?

Question

An eidolon normally gets Multiattack as a bonus feat if they have 3 or more natural weapons at level 9.

However, a Synthesist Summoner's eidolon does not have any feat of their own. So, my question is two-fold:

1. Does a Synthesist Summoner's eidolon get Multiattack as a bonus feat at all?
2. Does the Synthesist Summoner gain the benefits of Multiattack when fused with their eidolon?

Answer 1

"Multiattack" refers to two different rules items here. One is a class ability. The other is a feat.

As part of the Eidolon class feature, the Eidolon gains a special ability called "Multiattack" when the Summoner reaches 9th level. This is a special ability, not a feat.

The text of that special ability is:

An eidolon gains Multiattack as a bonus feat if it has 3 or more natural attacks and does not already have that feat. If it does not have the requisite 3 or more natural attacks (or it is reduced to less than 3 attacks), the eidolon instead gains a second attack with one of its natural weapons, albeit at a –5 penalty. If the eidolon later gains 3 or more natural attacks, it loses this additional attack and instead gains Multiattack.

The special ability grants a feat (also called "Multiattack") if the eidolon has 3 or more natural attacks. Otherwise, the special ability grants a second attack.

Can the Synthesist's eidolon gain that feat? No. The Synthesist's "Fused Eidolon" special ability says this:

The eidolon has no skills or feats of its own.

Therefore at 9th level, when a Synthesist's eidolon gains the Multiattack special ability, the effect depends on the number of natural attacks that the eidolon has.

• If the eidolon has 3 or more natural attacks, the Multiattack special ability has no effect for the Synthesist's eidolon, since the special ability would usually grant a feat, while the Synthesist's eidolon cannot have feats.
• If the eidolon has less than 3 natural attacks, the Multiattack special ability grants a second attack, as proscribed in the ability text.

Does the Synthesis gain the benefit of this ability? Yes. If the eidolon gains a natural attack via this special ability, then the Synthesist, when fused with the eidolon, gains that attack. From the Fused Eidolon class feature text:

The synthesist also gains access to the eidolon’s special abilities and the eidolon’s evolutions. The synthesist is still limited to the eidolon’s maximum number of natural attacks.

Answer 2

The eidolon can't gain the feat, but can grant it to the synthesist.

As noted in skoormit's answer, "Multiattack" is used to refer to two different things here: the Multiattack feat, and the Multiattack eidolon special ability (which can grant the Multiattack feat). While the eidolon itself is incapable of gaining feats, the Fused Eidolon feature does state that:

The synthesist also gains access to the eidolon’s special abilities and the eidolon’s evolutions. The synthesist is still limited to the eidolon’s maximum number of natural attacks.

As a result, instead of the eidolon gaining the Multiattack special ability, it instead grants that ability to the synthesist while merged. As a result, we can read the ability's text as follows:

The synthesist gains Multiattack as a bonus feat if it has 3 or more natural attacks and does not already have that feat. If it does not have the requisite 3 or more natural attacks (or it is reduced to less than 3 attacks), the synthesist instead gains a second attack with one of its natural weapons, albeit at a –5 penalty. If the synthesist later gains 3 or more natural attacks, it loses this additional attack and instead gains Multiattack.

So it would appear that, while merged, the Multiattack ability works normally for a synthesist, granting either a bonus attack or a bonus feat to the synthesist based on how many natural attacks the eidolon possesses.