Yes. According to the camera manual, if continuous shooting is enabled and you use the self-timer, the DSC-H300 can record a series of up to 5 images after one shutter press. That sounds like the feature your friend wants for changing poses between shots.

This is not the same as a remote-controlled interval mode, and it does not mean full app/remote support. It simply means the camera can start with the self-timer and then capture a short burst automatically.

The key limitation is timing: those shots are taken as a continuous sequence, so they may be fairly close together rather than several seconds apart. If enough time between poses is needed, that could be restrictive. But if the goal is just to get a handful of self-portraits from one setup, self-timer plus continuous shooting should work.