As in an alto range to a soprano range?
Depends on what you mean by "significantly". Vocal training will definitely help extend your range at either or both ends, but it won't change your basic physiology–your vocal cords, diaphragm, etc., which help to determine your voice's natural range & timbre.
I would say that vocal training could extend your range by half an octave or so on both ends, but if you're expecting to raise your reach by an octave or more, and you're naturally an alto, you may be somewhat disappointed. On the other hand, you may find that the soprano range (or most of it) is physiologically available to you & you just don't know how to access it. If you don't already know how to use your "head voice", you may have an upper range that you're not even aware of. I'm an alto in my upper range & a tenor/baritone in the lower, so on a good day I have a 3-octave range, from B-flat 2 octaves below middle C to a high A above the staff.
So go for the training–it can only help–but recognize that everything has its limits. And always do warm-up exercises to "stretch" your voice before you perform, so your full range will be ready when you go onstage.