You are probably on their informal waitlist. You might receive an offer even on 13-14 of April, contingent upon their first choices declining the spot. Conversely, you might receive a rejection as well, if they accept it. If I were you, I'd wait at least until then.
I really wouldn't recommend that you do that.
Ethically speaking, you would be ruining that spot for someone else, someone who might be considering that school as their dream school.
But more importantly for yourself, you should know that postgraduate research community is pretty small, and everyone knows each other in your prospective field of research. You will be in a community that constantly interacts with each other in conferences. People talk, and when your name comes up, people who's offer you've accepted, then declined will definitely talk about this. That will affect how people see you within the community and it may also affect your future prospects if you are known as the person who pulls this kind of stuff.
If you want to be proactive about this, you can contact the schools that have been silent and tell them that you have another offer that you have to respond to before April 15th and that you don't want to lose that opportunity, but you consider their school as your first choice and you will accept it immediately if an offer is made.
I know waiting is exhausting but you've made it this far. You wouldn't want to do anything that will harm you in the future based on an emotional decision.
I hope this helps.