No, this would not work. DisplayPort to HDMI adapters are only meant to be directly connected to your PC or docking stations. These are one-way adapters from a DisplayPort Source (computer or docking station) to be connected to a HDMI output (monitor, projector, television).

Using a DisplayPort to HDMI adapter will not add DisplayPort MST functionality to your HDMI monitor, as it is a feature of DisplayPort. HDMI does not natively support MST, and would be unable to do so even with an adapter.