Your evaluators just have to submit their letters to VMCAS before the October 1st deadline, independent of when you submit your VMCAS app. I think only one of my LORs had been submitted when I submitted my app, but all were in a couple weeks before the deadline so it wasn't a problem.
Vet schools seem to look favorably on applications, even if your end goal is not research. Mine definitely isn't, but in both of my interviews they asked me about my research and seemed to be genuinely interested in it.