Is there a way for GRSS to start tracking white items, or even just specific items?

For example in Karazhan on master looter we can't prevent members from looting Soul Essences or Motes of Mana for example, but we'd like to track how many they did loot and hold them accountable for that count (to be mailed to guild bank) at the end of the night.

Yes, there is a way to record any item that drops. Now, you might want to consider if you really want to see almost every item that drops.

Change the following from:
local GRSS_Colors={
--[[["ff9d9d9d"] = "grey",
["ffffffff"] = "white",
["ff00ff00"] = "green",]]--
["ff0070dd"] = "rare",
["ffa335ee"] = "epic",
["ffff8000"] = "legendary"
};

to (if you only want white to also be included):
local GRSS_Colors={
--[[["ff9d9d9d"] = "grey",
["ff00ff00"] = "green",]]--
["ffffffff"] = "white",
["ff0070dd"] = "rare",
["ffa335ee"] = "epic",
["ffff8000"] = "legendary"
};

or (if you also want greens):
local GRSS_Colors={
--[[["ff9d9d9d"] = "grey",]]--
["ffffffff"] = "white",
["ff00ff00"] = "green",
["ff0070dd"] = "rare",
["ffa335ee"] = "epic",
["ffff8000"] = "legendary"
};

Well yea. That's why I'm hoping for a way to just track totals of specific items instead of everything white and above.