I'm afraid you're out of luck here. CMake keeps this as an internal implementation detail, by design.
I'd say it's unlikely to change, but if you want to be absolutely future-proof, you could use a workaround of creating a static library out of the object files and then manually unpacking it back into object files (using the appropriate archiver/librarian) as part of the test. If the object files are also used by another target, and linking to that static library wouldn't work for that target, you can make an object library out of the files and then use that in both the original target and the for-test static library.
Here's an example of how you might achieve this workaround:
add_library(MyObjectLib OBJECT src/a.cpp src/b.cpp)
add_executable(Main src/main.cpp $<TARGET_OBJECTS:MyObjectLib>)
add_library(LibForTesting STATIC $<TARGET_OBJECTS:MyObjectLib>)
add_test(
NAME check-static-inits.sh
COMMAND ${PROJECT_SOURCE_DIR}/src/prepare-and-check-static-inits.sh $<TARGET_FILE:LibForTesting>
)
And here's what the script prepare-and-check-static-inits.sh
would look like (pseudo-code):
ar -x $1 -o some_dir
./check-static-inits.sh some_dir