Since Mars' atmosphere is around 2% the density of Earth's then could a much wider rocket achieve orbit?
Could the rocket be in the shape of a capsule or an optimal shape for reentry on Earth?
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Sure. Here is a model of a two-stage, liquid-fueled Mars Ascent Vehicle that was designed to fit efficiently inside a squat aeroshell. Hence the squat shape.
It did have somewhat of a fairing on the front to mitigate drag. That was enough to get it to work in the trajectory simulations with only a small drag loss.
Bloostar is released at around 20-40 km altitude. Surface atmospheric atmosphere on Mars is equivalent to around 35km altitude on earth. So aerodynamically there is no gross reason why you couldn't do it, and it could potentially open up the avenue to different shaped payloads if they don't have to fit into a skinny fairing.