Disclaimer, this is based solely on my experience as Tristana, i main her both ADC and APC and have varying success with her in low elo games (Silver III and below).
Depends on what you understand as "viable".
Can you win games with AP tristana? Certainly.
Can she carry on her own? Only early game and if fed through mid game. Late game she falls of due to her long cooldowns and lack of sustained damage.
She is pretty easy to counter (silence or any hard CC devastates her, kassadin, annie, talon, pantheon, ...) so you'll have to pick smart in champion select, make the enemy team think you are going ADC so you won't get countered or play safe and know the cooldown of you enemy champion.
The thing is in low ELO games most people either don't know how to counter or don't know how to play the champion that counters her so in low ELO this is less of a problem than in higher ELO.
Early game it's pretty easy to get 1 to 2 kills. At lvl2 just
AA, W, E + ignite (in air), AA, ... and you have a kill, and when your jungler ganks a kill is almost guaranteed. In most games I get first blood as AP tristana.
I teamfights it's little harder, problem is you'll have to jump right into the enemy team to assasinate your target since your burst probably isn't high enough to blow up the tank front line and the squisies are positioned in the back. Going around and then jumping on the backline from the fog of war or brushes is a good idea but not always an option when they are covering their flanks.
Roam, when you kill your lane opponent push the wave up to their tower (always a good idea) and roam top or bot and gank (with your jungler if possible). If you execute it good it's going to at least be one or two assists, perhaps a kill. Recall and by then you'll be lvl3 and item and lvl wise ahead of your lane opponent. From there on it's just rinse and repeat.
Go all in at lvl6 again when you have enough mana and your ult up, same combo but finish it with an ulti.
Mana is a problem, Tristana needs a lot of mana to execute her full combo (W, E, R) so not knowing how much mana you need is going to get you killed or at least makes you fail killing your opponent when you jump in and don't have enough mana for your ult to finish them off.
I always start Dorans Blade. It gives sustain, makes you win AA trades, makes last hitting easier and gives you a little extra health.
If I get first blood or more I always rush DFG, this item is simply OP on her, it makes your burst so much stronger, gives you decent CDR . Next is MPen boots and after that either Zhonya's or Void staff depending on the enemy team and playstyle.
I seldomly go Rabadons unless extremely fed, there are way beter options for Tristana that give her beter utility and damage than pure AP. Same thing for lichbane, her cooldowns are too high to make the most use of the spellbade passive and since I don't build rabadons the passive doesn't add that much.
Attackspeed/proc items are also a thing you can consider although i've had varying degrees of success with it. Malady's removal made Nashor's tooth interesting for tristana. Same thing goes for Wit's End. Both make her AA's do more damage which is a good thing but you'll probably want to build these only after your main build (DFG, MPen boots, Zhonya's and Voidstaff) so by then it'll make little difference. It looked good on paper when the Aatrox patch came out but it seems like it's pretty hard to pull off.