First of all, avoid using any vehicles, they get hard to steer pretty fast and you might pick coins by accident. So unless you are sure you can control your vehicle, either avoid picking them up or destroy them intentionally as soon as possible. In any event, turn off the magnetic vehicle add-ons if you have any.
Use powerups. Buy the Head Start powerup and when using it stay close to the ground. In my experience, 80% of the times you'll reach 750m without any coins. Grab a few Quick Revive powerups as well, use them only if you've reached a significant distance without picking any coins (say, 1250m). In the event you have a choice between death and picking up coins, die and revive yourself. I'd avoid using the Final Blast unless it's a last resort, you may end up collecting coins while you tumble away, in any case, don't use it if you have a Quick Revive unless you've used that first.
Picking up tokens is up to you, they don't count against you, and you might get a revive or a Final Blast in the slot machine, but if you use them and get coins or cash them in you'd lose your mission. I'd say - prefer to use powerups before spinning the wheel for the first time.
The mission isn't that hard, I've completed it successfully several times (I finished all missions 8 times by now), it's just takes a mixture of skill, luck and clever use of powerups.
Best Answer
Nope, it is fine as long as you keep it on your device it will still be there. (I haven't played in about 6 months and just checked mine, and everything is just how I left it)