The question really is "Are lifesteal quints worth it on AD carries?"
Tristana is actually one of the better early game carries. Her abilities doing magic damage is a boon in a few match-ups and she has a long range engage/escape. Even more so, her attack range starts out average and scales up to being higher than others.
I know that doesn't really pertain to the opening question, but I will address that as it is a seperate concern. Your basically asking how to play with trist against lanes that essentially are better than you in some way.
Against Draven: Avoid Q trades. Attack him after he has already attacked with a quick AA>E for some quick damage. Otherwise, just farm. Most Dravens are looking to all-in you early and have taken supports to match. Thankfully Trist has a good escape.
As for the Lifesteal question, sure they do. Lifesteal quints are one of the few scaling quints in the game comparatively. As you hit harder, they get better. But the base sustain from 6% lifesteal is actually really tiny. Even at 100 AD, your only healing 6 HP every attack. If you having issues with harass, consider HP5 quints instead to survive the early game or cloth armor start. As Trist, your probably gunning for end-game anyway. I personally use her all-in to win lanes with an aggressive support but I have not had the success playing Trist as I would like.
AD quints also just help with last hitting, the most important job in lane for any AD carry.