If I were holding out for a place at Matilda, I probably would only just book at the public hospital when I was 34-36 weeks or so personally... I'm kind of more of the opinion "why bother with something you may not need anyway?" And once you're in the system they want you to come to regular appointments with them as well which are a bit of a pain if you don't plan on delivering there...
I happen to disagree as I had fully planned to give birth in a private hospital--I was already booked to give birth there and had paid a deposit of $3,000 HKD and I had a doctor whom I was pleased with at the time. I was also registered with the public hospital.
In the end I am very glad I had also registered with the public hospital for two reasons. The first reason is that mid-way through my third trimester I started having problems and I needed very expensive, specific tests that are very rarely performed in the private sector. My doctor recommended these tests but said it would be not only extremely expensive for me if he ordered them but it would take a lot longer and the results may have to be processed in another city like Singapore or something. So, he recommended I seek to have these tests done in the public hospital. The tests were really important for me and the health of my baby. They were performed and the results were issued promptly. I didn't pay anything for the tests. They have the medical labs in-house (or through cooperation with the universities) to do the tests in HK.
The second reason is that when I was almost 39 weeks pregnant my doctor called me up and told me that he was not comfortable with my birth plan and basically bailed out on me as a doctor. At 38 weeks I toured the hospital I was booked to give birth in and realized it was totally not up to my standard of what I wanted for a birthing experience and also it was going to cost me almost three times as much as had been communicated earlier. So, I really had no choice but to go to the public hospital to give birth.
You can register at the public hospital and just make it known that you are seeing a private doctor for most of your appointments and then ask them which checkups you specifically should attend for their records. This is EXACTLY what I did in the beginning of my pregnancy.
I chose to see a private doctor for two reasons. The first reason was that the public hospital appointments are often inconveniently scheduled. You have no selection rights on day or time usually so in order to attend these appointments I would need to take a lot of time off of work and often on really inconvenient days to attend. It was a lot better for me to see a private doctor who is open in the evenings so I could go there after work.
The second reason was that when I was five months pregnant we decided to book a spot in a private hospital.
Anyway, when I registered at the public hospital at 12 weeks pregnant I told them I was seeing a private doctor (which is a common practice in HK anyway for women who are giving birth in the public hospital) and then I asked specifically what appointments I was required to attend in the public hospital--they told me that I needed to attend the structural scan at 24 weeks and take the blood glucose tolerance test at 28 weeks. They were totally fine with me not attending appointments there and just requested I get copies from my doctor of any tests or important records to bring with me when I went into labor. So, I could have registered with the public hospital and never given birth there and it really wouldn't have mattered that much to them. They're not going to call you up and ask you why you didn't give birth there if you eventually get into Matilda and they also aren't going to hound you about attending appointments. They have far too many people to deal with to do that.
Everything was going along
(I'm not telling you NOT to register, just saying you don't NEED to, ever if you don't want)