Not reliably with a standard Photoshop Action alone. Actions replay the same recorded steps, so if the source file placements were recorded, Batch will tend to reuse those same images rather than advance through a folder in sets of three.

For this kind of workflow, the better solution is a custom Photoshop script. Scripting can loop through a folder, open or place images three at a time into your template, save each collage, and then continue to the next set. If you expect to automate Photoshop tasks regularly, scripting is the right tool for this job.

If you don’t want to write code yourself, you could ask in a programming-focused forum such as Stack Overflow or hire someone to build the script for you.