I m not capable of answering this. But quantity surveyor and Civil engineer should be able to help you.
In development, it is quite common to have phase by phase completion. So technically this can be done and not much issues.
But no one can guarantee things for sure.
There is also different types of piling that some will less** affect nearby building.

We also have dilapitation report, where we survey nearby existing building condition. If ex building has cracks the owner wont take advantage and blame it on the new development. However if previously no crack and because of piling work, new crack is found then they will be liable.

Also, have u heard of highland tower incident?

https://en.wikipedia.org/wiki/Highland_Towers_collapse

What is your concern about the piling?

for residential condominium, example XXX Condominium that consist of 3 block, it has to be complete the 3 block then only it will get the CCC (certificate of completion compliance). then VP will take place and u get the key. however in certain scenario partial completion could be allowed by authority.

I believe u talk about different project. just another block built at adjacent to the completed 1.

u will never know whether they done piling or not as u have no access to the drawing. ur management office do have a set of as built drawing copy. which mean what had been actually built would be recorded in the that set of drawing. and this case u just need to have faith they done the work thoroughly. just like having faith when u cross the green traffic light, opposite car won't against the red light and bang u.

I think when they going to do the piling work, if there are building close to the project they will use hydraulic jack piling method. more pricey method of driving the pile. it won't cause much vibration like usual hammering method.

that would be unusual if 3 block within same project. example the 3 block should be sharing the same facilities like gym room swimming pool etc. that facilities completed?