aloh,
The minimum power supply for a Titan Z is 700W and while the z600 625W rating is probably conservative and the Titan Z may well run, the dual Xeon X5670's could not extract the full performance. On Passmark, the Titan Z has an average 3D benchmark of 7754. I am using a GTX 1070 Ti in a z620 running an 8-core E5-1680 v2 @ 4.3GHz and that has a CPU mark of about 17000 and 3D mark of 12132. The benchmark results are good because the z620 has a Passmark single thread rating 2273, but an I7-8770K running at 4.8GHz can make scores near three thousand and those will have 3D marks over 14-15000. For comparison, The average Passmark single thread rating or a Xeon X5670 2.9 /3.3GHz is 1346 with a dual CPU rating of 12353. Dual processor systems have lower single thread performance. If you are running simulations, or GPU rendering that are highly GPU oriented, the results could be quite good, but again will not make full use of the Titan Z and visualizaton applications and certinly gaming may be quite disappointing. Without liquid cooling there may be issues as well.
Overall, there would be much better performance level in every category: CPU- up tp 12-cores and Turbo speeds of 4.0GHz , Memory- DDR3-1866, fast 2D, 3D, Disk SATAIII, and USB (3.0) by buying a z420 or z620 that supports v2 Xeons. The best general cost/performance single E5-v2 CPU is the E5-1650 v2 6-core (about $130) having a CPU average of 12596 and single thread of 1994. Notice that the single 6-core E5-1650 v2 has a CPU mark higher than the two X5670's combined. The memory, disk system, and USB are all faster as well. If you need more cores, consider an E5-2680 v2, which is a 10-core @ 2.8 /3.6GHz Those are about $200 these days with a CPU 15737 and ST 1808. With a z620, adding a CPU riser board means the potential for a second E5-2680 v2: CPU = 21477.
This approach seems to be a much better investment, as the performance is much better and won't need replacement as soon. If you buy a used GTX 1070 Ti for $300-350, the residual $200-300 under the cost of a used Titan Z could buy the new CPU and more. A working dual Xeon z600 should be worth an amount within a reasonable range of a basic replacement z420 or z620. In effect, the overall project to have a much faster, future looking system is not a lot more costly. If you get a z620, you could add a second GTX 1070 Ti later.
BambiBoomZ