Sonic takes us well off the beaten track with this question! The only way to find out is to try it.
Although much is made of the brittleness of carbide inserts, modern ones are tough stuff. Breakages occur with heavy interrupted cutting, which causes high shock loads unlikely to occur in burnishing.
Most likely cause of failure I feel, is that Sonic’s inserts have a sharp cutting edge on one side. If this edge comes into contact with the work piece whilst burnishing, it will ruin the job by gouging deep into it. How likely, or not, it is to gouge depends on the job, how it is held, how the button is applied, and the skill of the operator.
Burnishing is a finishing operation, suggesting a lot of time already invested in making the part. Is it wise to risk spoiling it with a repurposed tool? Not done much burnishing, but in both cases I shaped a proper burnishing tool by grinding and polishing HSS. Key feature of my home-made burnishers – no sharp edges.
Dave