Technically, it should work because the pins on the HDMI connector can all mapped to corresponding pins on the DVI connector. Two things to note if using a DVI cable with adapter dongles for HDMI-to-HDMI connections:
- In general, using a dongle will degrade the signal as you lose something with each mechanical connection, so you won't be able to run as far of a cable run if using many dongles.
- There is no compliance spec or enforcement on DVI connectors and cables, so you may get a wider variability of cable quality when using DVI cables. All HDMI cables are required to undergo compliance testing and be meet the HDMI spec, and the HDMI Licensing LLC is taking an active role in enforcing these compliance requirements in products including cables & connectors.