There are slightly too many unknowns here for a straightfoward answer, but it can be shown that a continuous thrust transit (also known as a brachistochrone) between Earth's orbit and Mars uses up vastly more fuel than lifting from Earth's surface would, so the savings as a proportion of the fuel used are low.
Earth's gravity well to Mars, keeping 1 G of thrust the entire time (accelerate halfway and decelerate halfway).
Time: arithmetic says it'd take about 35 days.
You haven't thought very carefully about this! After 17 days of thrust at 1G, you'd be travelling at over 14000km/s and have travelled over 7 billion kilometres. The maximum distance between Earth and Mars is about 400 million kilometres. Your flight plan gets you to the Kuiper Belt, not Mars!
To travel the average Earth-Mars distance of ~225 million kilometres with a continuous thrust of 1G and a flipover in the middle takes a little over 3 days, given $t = 2\sqrt{\frac{d}{a}}$ where $d$ is the distance and $a$ is the acceleration.
However, if the ship were to launch from outside of the gravity well -- say, the L2 Earth-Moon-LaGrange Point -- how much fuel would be saved? Or, if using the same amount of fuel, how much time would be saved?
An important figure in rocketry is delta-V, or change in velocity. Earth's escape velocity, for example, is a bit over 11km/s. Ignoring the effects of atmospheric and gravity drag for the moment, a rocket which had a delta-V of 11-and-a-bit km/s could escape from Earth's gravity well and fly into interplanetary space. The moon's gravity is much lower, so its escape velocity is a bit over 2km/s. At the Earth-Moon L2 point it is lower still... well under 1km/s.
Now lets consider your 1G continuous burn trajectory. If we run the engine for ~1.75 days, we reach a maximum velocity of nearly 1500km/s. We then need to slow back down to a relative stop. That requires a total delta-V budget of nearly 3000km/s... slightly more than 270 times the minimum delta-V required to escape from Earth's surface!
Clearly, if you have rocketry powerful enough to sustain that much thrust for that long, getting out of a deep gravity well is a) child's play, b) cheap and c) fast. The difference will be negligible, if you ignore environmental issues.
You might consider asking a separate question about operating a rocket which could have a delta-V of the best part of 3000km/s inside Earth's atmosphere. Spoiler alert: it'll probably involve an awful lot of antimatter and be a bit like a continuous nuclear explosion that runs for a few minutes and probably ends with high-altitude EMP causing widespread issues across the hemisphere the rocket launched from. Rockets of this power level are exceptionally hazardous.