My question is: can opera singers change their voice sound with different techniques? Such as, can a coloratura soprano become a dramatic soprano by practicing with a different technique?
Voice is what you have and what you make of it. When both categories are well-stocked, a lot is possible as you can see with the example of Maria Callas.
Famously, at the beginning of her career, when she was singing Brünnhilda in "Die Walküre", Serafin called upon her to replace a singer fallen sick in the role of Elvira in "Il puritani", a part she never sang before, with six days of preparation. Again, you'll find the details of the story in the Wikipedia entry, but the long and short of it is that we are talking about drastically different vocal fachs here, and she executed both of them in the same season and I think with some temporal overlap.
I think you can, as far as you don't go out of your own register. A trained operatic singer knows how to handle its timbre (the harmonic properties of the voice) using different techniques.
Above the given example was Maria Callas. The male example is the great Plácido Domingo, which have sung roles for either lyric or dramatic tenor. Even light tenor roles. He also has an extended range that allows him to sing baritone roles, but that also means that he knows some special techniques that we low-voiced singers know.
A tenor rarely sings low notes (which for a baritone are like holidays), so they don't "care" about those notes. Baritones in the other hand, have to shine in each note and be rich in everyone of them but we don't like to get stuck with the high notes like our pals the tenors (besides that we can't sing that high).
Of course there are differences among the facher of each voice and some will depend of your physical composition, rather than just your own abilities. The thing with singing is that you have to be aware that part of the discipline of the singer is your own acceptance. Don't try to do anything that doesn't go with you.