You can, yes. Anecdotally I’ve heard stories of people doing so and receiving interview invites before their application was totally complete, but this was rumor. I have no confirmation.
I suppose the disadvantage is that once you submit it, there’s very little you can alter, change or add. I do think there’s good evidence for submitting well before the deadline, but I’m not sure at what point submitting early is just gratuitously early? Personally I aim to submit the first week of June, but which time hopefully all of my PEFs, my IEF and my transcript will be in.