I know of folks who have switched but you need to apply and I'm not sure how far up it goes. If you think you might possibly switch to Navy option then you should do it by the end of the first year as the Naval Science courses differ after that. You'll also still need to meet the other academic requirements ie. Calculus and Physics. I suppose your major can also play a role. If it's a Tier III major your odds will probably decrease but I'm just surmising that.
I have to say the switches are generally the other way but it has been done.