Yes, to improve your chances of getting a place, but also to experience how other places work.
What I was going to say about other unis is to contact potential supervisors and basically charm them so they like you and will help you with your proposal. This will improve your chances of getting funding as you will have them on side. Also, they will be expecting your proposal when it arrives at the uni.
Or put another way, think of what you can do to get ahead of the competition.