No way! 1A would most likely kill it instantly.
I measured two DX200s and they both drew from 550 - 730mA, depending on the batteries.
The DX lasers from TrueDX50 up all have the same pump diode, which is a 0.5W 808nm 9mm diode.
The power differences mostly come from the crystals and the alignment.
If you want less power to prevent modehopping, reducing the current might help, but it could make things worse.
If you're gonna change the alignment, it could actually resolve the modehopping and even make it more powerfull, but it's a very complicated and painstaking process, due to the way it is built. I wouldn't recommend trying, unless you have lots of experience and even more patience.
What kind of mode hopping problems do you have? How long does it take for the beam to split?
My first one would split in two beams instantly, the second would work up to a minute, but would split into four of five beams. With the second one, i could have resolved the modehopping with a slightly reduced current and better heatsinking, but it had abrupt brightness changes during warmup, so i returned it.
Depending on how yours behaves, there are different solutions for the problem.
But if you want to drive it from 3 AA cells, you would need a very low dropout current regulator. The easiest way would be to use a 317 circuit with two Li-Pos. A 317 won't work from 3 AA cells, unless you're talking about 14500 Li-Pos..
Another possibility, that would work from 3 AA cells is the AMC7135. But there you're stuck with 350mA, which would most likely be too little, and 700mA (with two AMCs), which would be too much, and you'd have to waste some current through a bypass resistor.
A safe current would probably be up to 600mA, but 500 would be safer, since i heard about one dying at 600..