If I were to install such a grab bar, I would add a sheet of 3/8" plywood on the inside of the cabinet and use machine screws with nylon lock nuts and fender washers.
You could, but I feel the cabinet itself would part at the seams before the screws would pull out using #8 screws with a pilot hole (or without.. its stronger! In particle board at least..)
http://9wood.com/files/rd_reports/screw_withdrawl.pdf Scroll down to the chart on page 10.
'low D' (low density, or the weakest) particle board with under torqued or properly torqued #8 screws will support 125 (weak torque, pilot hole) to 187 (proper torque, no pilot hole) pounds before pullout. The grab bars pictured use 3 screws each end, 6 total. So on the 'low' side, it would take ~600 pounds of force to pull that bar out.

I feel the cabinet structure would start to fail after the first 1/4 TON of force... (500 lbs)
1/2 inch drywall with the fanciest high load anchors?
""1/2” drywall - impact force applied at 600 lbs. downward force and 700 lbs. pull away force.""
Page 3 section 5.
https://www.moen.com/assets/moencom/documents/literature-center/BA0721.pdfAnother interesting observation from the same paper -
""Conclusion: Based on the research and testing done by North Olmsted reliability,
the speed a human can grip and hold a bar will never allow a load greater than 120% of the person’s body weight to be applied. 95% of the population will apply only 80% of their body weight. Therefore the performance of the bars far exceeds any real world load that would be seen during a slip or fall. ""
I am in the process of installing grab bars all over our house for a disabled relative who now lives with us. Been doing some research.

I tend to overbuild, and to ridiculous lengths sometimes. Trying to do better design engineering now.