I tried Draven the other day on my friends account and he was actually pretty fun. The only problem is that I can't for the life of me, catch his axes consistently while chasing or in a teamfight. If I can't do that, how much of a disadvantage am I at? Is it absolutely necessary to keep his Q active to match up to the other ADCs?

Just practice and you'll be k.

I haven't done the math or anything, but I'd assume Draven is subpar if you aren't at least making some effort to catch the axes. Just keep practicing and you'll get better.

exactly, just practice and you will get better

axes take about 1 second to fall down i believe, one thing i would recommend is to use your (w) before throwing the axe , and it will increase your movement speed and attack speed temporarily and allow you to catch your axes easier.. Also when you catch your axe it will remove the cooldown on your (w) so you can just keep spamming it to help catch your axes.

hope that helps.

also the returning axe is going to land in a direction of where you character was facing when the axe hit. so if you want the axe to land behind you on its return trip then after you throw it , instantly start facing draven away from where you are and your axe will land behind you. same goes for any direction.. This specifically applies when chasing an enemy, typically your axes will land in the direction that you are chasing the enemy in. .

Catching while chasing shouldn't be too hard as the axes go in the direction you are traveling right after you throw your axe. However, team-fights are always going to be rough for Draven. Try and aim your axes to land in a relatively safe spot that you don't think is in CC or stun range. I always walk sideways after an attack, that way the axe is closer to me and is in the same relative range. Walking backwards greatly delays your attack speed and standing still is suicide. If you have to though, don't be afraid to walk backwards.

Honestly, Draven's damage doesn't' fall off too much without his axes - he'll be about on par with most ADCs if you don't use them. So think of using axes for the first two-three hits and then focusing on positioning and chasing. If you get those first two or three axe-hits your damage will greatly outscale any other ADC. Then just finish off with auto attacks.

Also, practice with axes as much as possible - you have a whole laning phase to just play around with your mini-game. Take advantage of that. Sometimes I juggle two axes in lane phase just to get better at it.

honestly all you need to do is juggle as much as you can and use your w at all times cause with a catch the cooldown is refreshed and u have as and ms for days/ honestly juggling your blades is amazing and gives you such an advantage over any other adc. but yeah like the other dude stated practice it and you will win games