No. Most DisplayPort to HDMI cables and adapters are one-way adapters from a DisplayPort Source (computer or docking station) to a HDMI Sink (television, computer monitor, or projector).  These cables do not work in reverse.

DisplayPort uses packet-based data transmission, breaking the video stream into individual packets of data allows for longer cable runs, use in both copper and fiber-optic cables, and allows for higher bandwidth than other video formats.  It is relatively easy to convert from DisplayPort to HDMI (computers with HDMI output ports already do this internally) and dual-mode DisplayPort outputs have built-in adapters to  output a HDMI signal for use with passive DisplayPort to HDMI adapters.

HDMI uses a video signal, similar to DVI, this requires more power to operate at the same cable lengths as DisplayPort and requires significantly more processing power to create DisplayPort packet-based data.

Externally powered HDMI to DisplayPort adapters do exist, these generally have a USB or small barrel plug for power, and can convert from a HDMI Source to DisplayPort Sink.  In most cases they have reduced resolution or refresh rates compared to modern signal sources and can introduce delay in the data connection between the display and computer potentially causing reduced connectivity or display performance problems.

We do not currently recommend using HDMI to DisplayPort adapter with our docking stations.  In our testing they have been unreliable compared to a native DisplayPort connection.  Many of our  newer docking stations include both HDMI and DisplayPort outputs to reduce the need for additional adapters or adapter cables.