Yes, I believe this has been accomplished already. But what would be the advantage? 6th gear in the 6-speed is the same overdrive as the 5-speed, plus you'd have one more gear to shift into. The gear spacing is closer that's all, but I am not sure about the final drive. That may be a different ratio.

 

The 2011 Mazdaspeed3 brochure indicates these ratios:

Gear / Ratio / Final Drive / Overall
...1st / 3.21 / 4.19 / 13.47
...2nd / 1.91 / 4.19 / 8.02
...3rd / 1.37 / 4.19 / 5.72
...4th / 1.03 / 4.19 / 4.29
...5th / 0.95 / 3.53 / 3.35
...6th / 0.79 / 3.53 / 2.79