Very unlikely. HDMI only adapts to single-link DVI, and the HDMI device will most likely downclock to 165MHz for compatibility once it detects the DVI input on the other side. 120Hz is only possible with either the 340MHz pixel clock of HDMI 1.3+, or the second data link you get with dual-link DVI. With an HDMI-to-DVI adapter, you don't have either one. Doesn't the XL2411T have an HDMI input? If you use a straight HDMI connection you can probably get 120Hz working.
5/14/15 at 11:21pm