I don't know if you have this model or not but here are the specs:
 
http://www.cnet.com/products/alienware-aurora-r4-core-i7-3820-3-6-ghz-16-gb-2-tb/specs/
 
The specs indicate an 875 watt PSU. If this PSU provides a minimum of 42 amps on the 12 volt line then it should work. The specs should be shown on the PSU itself on the side.
 
However DELL motherboards are made strictly for Dell so I hope that video card will work. A motherboard BIOs update would be wise if there is one available.

R4 has a 875W power supply.  I have one for my old rig and have used both 780 reference card and 780 Classified cards on it and both worked no issues.  I would assume the Titan Black should work fine, but I am not positive.

Technically R4 is 3.0, but since it runs the X79 chipset, Nvidia has only officially supported 2.0 speeds due to some variances between motherboard manufacturers.  This issue originated back in the 600 series cards and X79 platform still running Sandy Bridge-E (3820, 3930K, etc...) chips still isn't technically supported under 3.0.  But there is a patch that can be run to force enable 3.0 speeds.  See the link below.  I have used this on my R4 and have had no issues and does enable 3.0 speeds.  Ivy Bridge-E (4820K, 4930K, etc..) chips do support native PCI 3.0 speeds.
 
Download the patch and run the executable.  You may need to run as administrator.  Reboot and then do the render test in GPU-Z and it should report at 3.0 speed.
 
http://nvidia.custhelp.com/app/answers/detail/a_id/3135/~/geforce-600-series-gen3-support-on-x79-platform
 
Honestly though, on a single card setup, the difference between 2.0 and 3.0 is very minimal.  Even at 2-way SLI it doesn't make a big difference, maybe 10% or less.  Once get into 3 or 4-way SLI is when it really makes a difference.
 
Hope that helps.
 

Question do you just game? If so do not get a Titan *shakes head* Get a GTX 780 TI or a GTX 780 6gb card when it comes out you will be a lot happier over a Titan. Titan's are for those playing at insane resolutions with multiple monitors, or for those who do a lot of 3d work be it maya/max or any other autodesk product, those that do gpu rendering, particle, water, and hair simulations, Those that use directcompute. If you do not fall into that category I would suggest saving some money and going with one of the cards I suggested.