As Russell Borogove pointed out, that plan is quite impossible because you need to get that mass from somewhere, and all the other mass is already concentrated on even larger planets. And even when we would have enough asteroids, the plan would still not be even remotely feasible due to the huge energy requirements it would take to change the orbits of such huge amounts of mass.
But let's assume that this plan would be possible and examine it theoretically.
When there is a plastic collision (two bodies crash into each other and turn into one), not only their masses combine, but also their momentum. Depending on how they hit, this will result in a rotation and velocity change. So yes, every asteroid impact changes the planet's speed (and thus its orbit) and its rotation.
However, when you plan the asteroid strikes properly, you can plan them in a way that they cancel each other out and the resulting body has the same orbit and rotation as the original one.
Also, another question remains: Is the resulting body still Mars? To get a surface gravity of Earth, you would have to increase the mass by factor ten. So just 10% of the mass would be original Mars material, the rest from the asteroids you scooped up. So the composition of the new planet's soil and atmosphere would depend far more on your choice of asteroids than on the original properties of Mars. All the asteroid impacts would also generate a huge amount of heat, so you would end up with a hot, geologically unstable mess of a proto-planet, which will take millions of years to cool down.