It depends- if it is a CNM, yes, otherwise no (as far as Im aware). You could also see an OB or CNM just earlier in the pregnancy then transfer. The home birth midwife will have other things to offer, like ginger, acupuncture, magnesium supplement, etc. I had awful vomiting with my DD, and did all the non-prescription stuff and it was miserable, I was totally incapacitated until about 16 weeks, although I guess fine overall in that I never needed IV hydration or anything. With a 2nd pregnancy though I had Zofran available and it was amazing. That pregnancy ended in a miscarriage (unrelated to the zofran) but I plan on using it for upcoming pregnancies.
I think it may depend on where you are located and what kind of a midwife you use as legislation varies. That would be a good question to ask during the initial interviews with midwives actually. You could also consider shadow care (is that what it's called?) at the same time with an OB or family doctor, perhaps just during the early part of the pregnancy or whenever you have morning sickness.
If you want stronger meds than your midwife can provide, which depends on the laws in your state, then simply go to your regular doctor and ask for them from her. Just tell her that you want care for this one medical issue, and that your regular pregnancy care will be handled by your midwife.