The Blinded condition affects Ability Checks that rely on sight. It says nothing about Saving Throws, so you can make a Saving Throw just fine, of any kind.
The synthesist gets nothing from the eidolon's saves, and only part of its ability scores.
From the PFSRD:
Fused Eidolon
...
While fused with his eidolon, the synthesist uses the eidolon’s physical ability scores (Strength, Dexterity, and Constitution), but retains his own mental ability scores (Intelligence, Wisdom, and Charisma). ... The synthesist uses the eidolon’s base attack bonus, and gains the eidolon’s armor and natural armor bonuses and modifiers to ability scores.
There's nothing in there about saves. If something gives the eidolon a bonus to saves (such as the progression eidolons get as the summoner gains levels), the summoner gains no benefit from it. It doesn't matter which saves are the eidolon's good saves: the synthesist does not get those bonuses.
A synthesist will tend to have higher saves than other summoners though, thanks to ability scores. Because she uses her eidolon's Dexterity and Constitution ability scores, she will use its modifiers in those abilities rather than her own (which are likely to be lower). This will tend to give her higher reflex and fortitude saves than she would otherwise have.
Shielded Meld (which kicks in at level 4, incidentally, not level 2) does improve the synthesist's saves, because it explicitly says it does.
Thus, a level 4 summoner would calculate her saves as follows (while fused with her eidolon):
- Fortitude: +1(summoner) +C(eidolon's Con modifier) +2(shielded meld)
- Reflex: +1(summoner) +D(eidolon's Dex modifier) +2(shielded meld)
- Will: +4(summoner) +W(synthesist's Wis modifer) +2(shielded meld)
(Plus any other bonuses, such as from magic items, feats, traits, etc.)
TLDR: Synthesists are already ridiculously broken; don't make it worse by giving them bonuses to saves they're not supposed to be getting.
Best Answer
While spell attacks are affected by the unseen attackers rule (PHB 194) as any other attack, saving throws follow different rules. In the general rules for saving throws we read that:
But while it is left up to the DM, there is also the arcane trickster feature magical ambush:
It is strongly implied that this is a special rule overwriting the general case. Granting this to all characters (and NPC-s) would make this feature redundant.
There are not many features that grant disadvantage on saving throws. The above rogue feature is acquired on level 9, and the sorcerer metamagic that does it is generally the most the expensive one. It is clear that such a thing should be regarded as really powerful. Consider that traps also grant a saving throw as normal, even though they need no components to cast and are usually hidden.
Thus I advise against ruling that being hidden should grant disadvantage on saving throws.