As a followup, I did some research on WoWhead, and cross-referenced it with what I could find on Twinkinfo about available gear (as some gear never made it out of previous betas, but is still listed on WoWhead). Note that a lot of what I found is white gear for sale by vendors, and features higher item levels. Here are slots and their associated item levels (in parenthesis), potentially attainable at level 1, and useful up through at least level 39:
Head: (90)
Mist-Piercing Goggles - Item - World of Warcraft
Neck: (80)
Problem Solving Pendant - Item - World of Warcraft
Shoulders: No significant finds
Back: No significant finds
Chest: No significant finds
Wrist: No significant finds
Hands: No significant finds
Waist: No significant finds
Legs: (35)
Haliscan Pantaloons - Item - World of Warcraft or
Tuxedo Pants - Item - World of Warcraft
Feet: No significant finds
Rings: (60)
The Rock - Item - World of Warcraft
Trinket1: (60) Insignia (the class-based PvP trinket bought with honor)
Trinket2: (55)
Arena Grand Master - Item - World of Warcraft
Weapon: No significant finds
Off-Hand: (60)
Bouquet of Black Roses - Item - World of Warcraft (among others). If a lower level character can get summoned into the WoD version of Shadowmoon Valley, then
Bouquet of Dried Flowers - Item - World of Warcraft offers iLevel 90.
If your typical 19 twink goes from an average item level of 26 to an average item level of...let's say 46 for the sake of argument (and easy math), we're talking about a 20 * 0.1% stat improvement in Legion, or 2%. Which is to say, very little.
...This is assuming that the granddaddy of all item level crushers gets nerfed in Legion, as mentioned in the original post:
Kor'kron Shaman's Treasure - Item - World of Warcraft
If the Kor'kron gear retains its item level in Legion, now we're talking closer to a 30% stat difference.
Edit: Thanks to Warglaive, I just saw the tweet confirming lower level PvP will also use PvP templates:
https://twitter.com/WarcraftDevs/status/671499968079785984