My prospective supervisors are not emailing back, should I just submit a PhD application anyway? Context: I want to do my PhD in Hong Kong. Only one University there (University of Hong Kong) explicitly states you need to contact a supervisor and discuss a research proposal before you apply. The others, at least in my field, do not even require a research proposal for your application.

Regardless, I obviously am trying to get faculty members to agree to supervise me and discuss PhD topics to strengthen my application and ensure that a suitable supervisor is available. 

The trouble I am facing is that only a few of those I have emailed have replied, and the ones that did reply said they already had too many PhD students or weren't taking students on at the moment. Looking at current PhD students, >95% of them are Chinese so I suspect part of this might be unwillingness to take on a foreign student (or just preference for Chinese students) despite Hong Kong being a very multicultural city.

I would like to live and work in Hong Kong after my studies, which is why I am set on doing my PhD there.

My question is this: How much does it hurt your chances of admission to not have a supervisor pre-arranged before you apply? I feel that my grades, references, experience are very competitive, but I am worried about this roadblock.
I know your feeling, I was in your situation once.

Thing with Asians universities (far east and south east)
They will not reply to your email unless they know you, or even if they are corresponding authors and you ask them something, they will never reply. That is my experience and in general, I think you should meet them through conference attendance and research work.
The University of HK is regarded top tier in the world, I don't know much what is your field, but I assume they get tons of emails.
Generally, for China, if you are self-funded student, they will allow you to apply without supervisor consent, but if you need scholarship, Acceptance letter is MUST have, this is same with MC, Taiwan, Japan, Singapour and others