You have raised a very interesting question. I am going to discuss it on the premise that program you mentioned is a four-year program which leads to a bachelor's degree. A two-year associate program would not be appropriate as few, if any, of its credits would transfer to a university pre-vet program.
If you had asked about a four-year bachelor of science in nursing program, my answer would be that it is not an appropriate pre-vet major. Medical schools and presumably veterinary schools would consider your going on for a career other than nursing to be a waste of an educational experience and degree which could have been awarded to a person who would go on to become a nurse. They would hold the nursing degree against the applicant.
I cannot see any valid distinction between nursing and diagnostic sonography in this context. So my conclusion is that diagnostic sonography is not a good pre-vet major.
May I suggest animal science, chemical engineering, biological engineering, and biomedical engineering as pre-vet majors which will provide good preparation for veterinary school as well as good career opportunities, which will pay much more than diagnostic sonography, for the more than five out of seven veterinary school applicants nationwide who are not admitted to any veterinary school.
First of all, those are three very different programs, and schools might only offer a few if any of them. Second, you must do your medical training in the country in which you live and plan to work. It does NOT easily transfer to another country. If you're not a US citizen, you can pretty much forget about med school here; most won't take foreign applicants.
You can major in nursing in college if you want to be a nurse. That's how you become a nurse. To be a doctor or a vet, you'd major in anything in college (but NOT nursing) and take the pre-med or pre-vet classes. Then you'd apply to medical or vet schools after college. Both are extremely competitive programs; going to a school for your bachelors doesn't mean you'll get in for med school. Sure, there are some great programs you could be applying to in 4-7 years, depending on where you are now. But most people are lucky to get into any program, since so many won't get in at all. You usually can't be picky.