In OD&D, I can't find much clarity as to the effects of invisibility at all.
In BECMI, you have a -6 penalty to hit an invisible defender. And you can't see them. The rest is up to you. Don't see any impact on saving throws. (That -6 may be from the Rules Cyclopedia).
In 1e, you have a -4 penalty to hit an invisible creature and have to detect them with a percentile roll based on your level/HD and Int per the "Detection of Invisibility" table, or they give themselves away in a manner adjudicated by the DM. And,
Any attacks incur the -4 penalty of attacking on
invisible opponent, of course, and the invisible creature likewise is
entitled to +4 on saving throws. - 1e DMG, p. 60
In 2e, you have a -4 penalty to hit an invisible defender and have to detect them by a save vs. spell, which lets you know their general vicinity. No saving throw effects I can find.
In 3e/3.5e/Pathfinder, an invisible target has total concealment and therefore enemies have a 50% miss chance, and they have to use Perception to target you in the first place if it's a targeted effect. There is no modifier to saving throws. (Cover, not concealment, gives Reflex save bonuses.)
In 4e, an invisible target has total concealment and therefore enemies have a -5 to their attack rolls, and they have to use Perception to target you in the first place if it's a targeted effect. In 4e, magical attacks are against various defenses, saving throws are only for ending ongoing conditions, so no, invisibility doesn't affect saves, but it does affect the mechanic which does what saves did in earlier editions.
So I guess in short - "Only in 1e."