"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.