Does the Periodic Structural Inspection look at cracks?
Yes. BCA's PSI guidelines require the engineer to record signs of structural defect, deformation or deterioration, including cracks, comment on their extent, likely causes and seriousness, and classify them as of no structural significance, needing remedial action or monitoring, or needing full structural investigation. Unit owners in strata developments can ask, through the MCST, for the appointed engineer to inspect their unit.
From the RRD Field Guide, checked against the sources cited in Cracks in Walls, Beams and Ceilings in Singapore: Which Are Structural and When to Worry. General information, not advice for your project.
The fuller picture
Most hairline cracks in plaster, paint and at wall-to-beam joints are non-structural, caused by shrinkage and thermal movement. Worry when cracks are wide or widening, diagonal or stepped, tapered, recurring, accompanied by rust stains, sagging or sticking doors, or appear in beams, columns or slabs. Monitor with dated tell-tales and call a Professional Engineer for those signs.