Not necessarily. Bows were made obsolete by the simply use of firearms, namely, the aiming (In the loosest sense of the word, with the horrible accuracy of early firearms) and pulling the trigger. A good bowmen would take a lifetime to train and be of use in a war, while any chump could be trained to hold a musket. Early firearms made armour more or less obsolete, not bows, which were used enough until the pike-and-shot era.

For those that seem to think that arrows should do less damage than a bullet, remember that an arrow is essentially a slower, heavier, and larger bullet. That wedges yourself into you. It hurts. With it's size, nerve and muscle damage is sure to occur, which more or less incapacitates anyone who gets hit. You don't pull out arrows from yourself as if they were minor inconveniences, like in the movies, you fall on the ground in agony from the shock, and the amount of force inflicted by it.

Muskets fired slower-moving projectiles than modern guns. Using non-direct fire, a bowmen would most likely outrange a musketeer, who could theoretically try aiming his gun at a silly angle, but wouldn't do much good. The main thing is accuracy. At far range, the arrow will still fly straight at it's target in an arch, while a musket ball will have begun to fly wildly long ago. Effective range is exactly that. Effective range. Farther than that, you may get one or two stray shots, but the vast majority of bullets end up plowing into the ground, or going nowhere near the intended target.

The main problem with the natives is their huge stockpile of manpower to attack you with. Surprisingly enough, it is their numbers that actually makes it annoying to fight them, not their troops, which are only average.