Why would you need to accelerate anything at 1 g? That's a ridiculously high acceleration for getting to Mars. What matters more is the total delta-V, and if it can deliver it in time short compared to the transit time to Mars.
High Isp solar electric systems would not exploit the Oberth effect (likely they would start in high Earth orbit) so they don't have a high acceleration need from that.
If you want to accelerate to 15 km/s in 1 week, that's 2.5 milligees.
Accelerating/decelerating at 1G the entire journey would be the perfect scenario. Not only that would be the shortest travel time, but it would maintain gravity inside the ship all the time. If this is not the ultimate goal being worked towards, then we may as well just give up now. Nuclear is where it's at - it's the most efficient weight to power ratio generation known to man.
It's about as realistic as propelling the vehicle with unicorn farts. In particular, the kinds of nuclear propulsion being discussed in this thread could not do it. Solid core nuclear thermal rockets using hydrogen have an Isp of about 1000, so they could accelerate a vehicle at 1 gee for less than an hour.
The power/weight ratio of nuclear rockets actually sucks, compared to chemical rockets. Conveying heat through a solid/fluid interface is awkward and slow compared to just making it in situ by combustion.
