Does adding the Half-Construct template to a race change aging in any way?
Apparently not! The half-construct option comes with the following:
No aging is mentioned, which makes sense, since half-constructs are only "artificially enhanced or have parts replaced by constructed mechanisms, be they magical or mechanical." They're still organic to some extent, and their organic parts still age.
Strangely enough, though, the original construct type doesn't mention anything about aging either.
How a particular construct or half-construct character ages may be something for the character's player to work out with their GM. If a person has only a few parts made construct, then aging will probably still affect them significantly - but if most of a their physical body has become construct, then they will probably would remain physically well far into old age as long as they can keep on affording maintenance and new parts.