Would more questions regarding the planet be answered if this was the case?
I'm going to say no, for a few reasons, but if anyone wants to give a more detailed answer, feel free.
1) Planets and moons that form inside the frost-line have much less water and other ices than those that form outside. Mars likely once had water and oceans but if it had formed outside the frost-line it should have a lot more water and a lower density. The frost line moves away from the sun as the sun grows more luminous and planets move, so there is a degree of imprecision with this argument, but I believe this on it's own is a pretty good reason why it's not likely.
2) A moon that escapes Jupiter's orbit should enter a near Jupiter orbit initially, and at some point later, it could receive a gravity assist and be propelled either in towards the sun or away, but it's unlikely that Mars could have obtained it's relatively circular orbit had it originated as one of Jupiter's moons, unless Jupiter was much closer to the sun when Mars escaped.
3) it's difficult to see how the asteroid belt could have stayed around if Mars originated outside the asteroid belt and moved inside it. Mars passing through the asteroid belt would have caused significant disruptions to it.
Yet another indication that Earth and Mars formed in the inner Solar System is that they have the same deuterium to hydrogen ratios. Primordial water trapped in 4.55 billion years old (0.017 bn years after Earth formation) lava from the deep mantle has been compared with Martian meteorites. The ratio should increase further out in the Solar System.