I tried Agner's train delay patch (https://bugs.freedesktop.org/attachment.cgi?id=92883) with the recent linux-3.13.2 and had partial success with a HDMI connection.  My rig includes T440s with a ThinkPad Ultra Dock.  As noted by others, the display is not instantly turned on; it takes about ~30 seconds to light up.  I say partial success because the display now has patterns with green dots all over.  See the attached picture I took with my camera (https://bugs.freedesktop.org/attachment.cgi?id=93654).  I green overlay is also present with Pichler's patch (https://bugs.freedesktop.org/attachment.cgi?id=91164), but I only observed it once.

I observed the following in dmesg:
root@iris:/home/totakura# dmesg | grep drm
[   17.327337] [drm] Initialized drm 1.1.0 20060810
[   17.566302] [drm] Memory usable by graphics device = 2048M
[   17.607126] [drm] Supports vblank timestamp caching Rev 2 (21.10.2013).
[   17.607128] [drm] Driver supports precise vblank timestamp query.
[   17.746991] [drm] GMBUS [i915 gmbus dpb] timed out, falling back to bit banging on pin 5
[   17.764706] fbcon: inteldrmfb (fb0) is primary device
[   18.782531] [drm] Enabling RC6 states: RC6 on, RC6p off, RC6pp off
[   19.354891] i915 0000:00:02.0: fb0: inteldrmfb frame buffer device
[   19.363836] [drm] Initialized i915 1.6.0 20080730 for 0000:00:02.0 on minor 0
[  466.978775] [drm:intel_dp_complete_link_train] *ERROR* failed to train DP, aborting
[ 1216.132474] [drm] stuck on render ring
[ 1216.132490] [drm] GPU crash dump saved to /sys/class/drm/card0/error
[ 1216.132493] [drm] GPU hangs can indicate a bug anywhere in the entire gfx stack, including userspace.
[ 1216.132495] [drm] Please file a _new_ bug report on bugs.freedesktop.org against DRI -> DRM/Intel
[ 1216.132497] [drm] drm/i915 developers can then reassign to the right component if it's not a kernel issue.
[ 1216.132500] [drm] The gpu crash dump is required to analyze gpu hangs, so please always attach it.

I could not get the GPU crash dump which is show in the dmesg as I rebooted immediately.  Sorry :(

Next, I combined Agner's (92882) and Pichler's(91164) patches into one (https://bugs.freedesktop.org/attachment.cgi?id=93653).  With this patch, I was able to boot up while docked.  The transition from GRUB to FB took a while but after that the external display is identical to that on the notebook display.  Consequently, I was able to suspend/shutdown while docked.  While waking up from suspend there is also a delay during which the system freezes, but its short.  With this patch I do not see the DRM warning in dmesg anymore.  This is the output now:

totakura@iris:~$ dmesg | grep drm
[   19.758646] [drm] Initialized drm 1.1.0 20060810
[   20.152088] [drm] Memory usable by graphics device = 2048M
[   20.192418] [drm] Supports vblank timestamp caching Rev 2 (21.10.2013).
[   20.192419] [drm] Driver supports precise vblank timestamp query.
[   20.320274] [drm] GMBUS [i915 gmbus dpb] timed out, falling back to bit banging on pin 5
[   20.426013] fbcon: inteldrmfb (fb0) is primary device
[   21.811554] [drm] Enabling RC6 states: RC6 on, RC6p off, RC6pp off
[   43.744150] i915 0000:00:02.0: fb0: inteldrmfb frame buffer device
[   43.768082] [drm] Initialized i915 1.6.0 20080730 for 0000:00:02.0 on minor 0

With the external display working over HDMI, I went on to connect another display to the VGA port on the dock.  This display simply replicated the HDMI display.  This should not be the case here as from the dock's manual, I should be able to drive three displays, of which one should be connected to the VGA port.

I also observed that even though I connected to the HDMI port, the xrandr output still lists the external display under DP2 while showing HDMI2 as disconnected.  I do not know if this is a bug or not.  Here is the output:
totakura@iris:~$ xrandr
Screen 0: minimum 320 x 200, current 3840 x 1080, maximum 32767 x 32767
eDP1 connected 1920x1080+1920+0 (normal left inverted right x axis y axis) 309mm x 175mm
   1920x1080      60.0*+   59.9  
   1680x1050      60.0     59.9  
   1600x1024      60.2  
   1400x1050      60.0  
   1280x1024      60.0  
   1440x900       59.9  
   1280x960       60.0  
   1360x768       59.8     60.0  
   1152x864       60.0  
   1024x768       60.0  
   800x600        60.3     56.2  
   640x480        59.9  
DP1 disconnected (normal left inverted right x axis y axis)
HDMI1 disconnected (normal left inverted right x axis y axis)
DP2 connected 1920x1080+0+0 (normal left inverted right x axis y axis) 598mm x 336mm
   1920x1080      60.0*+   50.0     59.9  
   1920x1080i     60.1     50.0     60.0  
   1680x1050      60.0  
   1280x1024      75.0     60.0  
   1440x900       59.9  
   1280x960       60.0  
   1280x800       59.8  
   1152x864       75.0  
   1280x720       60.0     50.0     59.9  
   1024x768       75.1     70.1     60.0  
   832x624        74.6  
   800x600        72.2     75.0     60.3     56.2  
   720x576        50.0  
   720x480        60.0     59.9  
   640x480        75.0     72.8     66.7     60.0     59.9  
   720x400        70.1  
HDMI2 disconnected (normal left inverted right x axis y axis)
VIRTUAL1 disconnected (normal left inverted right x axis y axis)

With the other display connected to VGA, it is not listed by xrandr.

Apart from these, sound via HDMI is working.  Note that the sound output from the dock via 3.5mm pin is disable when HDMI is in use.