Spectres that summon totems?

If my spectres summon totems, will supporting Raise Spectre with gems like Efficacy, Burning Damage, Minion Damage, and etc. increase their totem damage? (I'm using the Scorching Ray totem spectres.)

Yes. Totems use their creators offensive stats for damage so anything affecting the spectre's damage will affect its totems damage.

Minion and Totem Elemental damage is particularly good with those guys as it will:
Give the spectre the stat "+% elemental resistance".
Give the spectre the stat "% more elemental damage" which will affect the damage of the totem it places.
Give the spectre the stat "+% elemental resistance of your totems".
Give the spectre the stat "x% more elemental totem damage" which of course also affects its totems damage.
So about 45% elemental resistance to both the spectre and its totems and around 40% more elemental damage from the searing beams.

You can also get them to summon 2 totems by using Tukuhama's Fortress with Necromantic Aegis or if you're playing as a scion by socketing them in your helemt and picking the hierophant ascendancy passive.