If you pass your test on an automatic then your licence will state that as one of the restrictions. If you look at the HK Driving Licence (you do have one, don't you?) on the back you will see in the list of Vehicle Classification Codes the type "A" which means "Automatic Transmission". If the List of Full Classes for which you are licensed on the front of the licence says "1 2" then you can drive any car or light goods vehicle. But if you pass your test in Hong Kong (or in the UK, I don't know about other places) on an automatic vehicle then the Full Classes will be "1A 2A" which means you are only licensed to drive vehicles with an automatic transmission.
I think they would if the original licence has that restriction. I know that UK Automatic only licences exists so presumably that transfers to HK.
However, I suspect that in the US the licences don't differentiate manual and auto, so even if you have never driven a manual car in your life, when you transfer to a HK licence it would be unrestricted. This is obviously a limitation of the "direct issue" transfer system.