I think it would definitely be helpful to have the Masters degree, but you could always stop for a moment and have one year where you do consecutive interpreting.  As Laura Wilkinson  said you need the certifications and the courses to get to the level you need to be a simultaneous interpreter. 

But you can also look for any volunteering opportunities for something that you're interested in and then perhaps further your knowledge by studying the Masters course

We do have interpreters on our books that have worked on public service interpretation, so they've got their public service qualifications for consecutive work, they've amassed a lot of hours in that consecutive environment with social services, police and courts work, and they've really taken to it. They've then moved across in simultaneous interpretation, but they've done that generally via a Masters degree.

So you have that opportunity to build up some work experience within the industry and you'd get to know if interpreting is for you before you take that deep dive and enrol on a Masters degree. So asKalina Raeva said, it gives you a little space to test the water, build up your knowledge, find out if it's for you which is absolutely key to being successful.