No, this isn't going to work since the DI output is balanced and the adapter will put inverted signal on the ring and the non-inverted signal on the tip. Most simple interfaces won't allow you to invert the ring then sum (assuming a stereo 1/8" input, and I don't know of any balanced 1/8" inputs).
Assuming you have a D-800+ or WD-800, what you can do is take the effects send and since the send's ring floats, you will get a good signal in the tip. This will be a line level signal so be sureto setthe laptop or interface to receive line level.
For using the DI in this situation (assuming you have access to quality soldering equipment and technique):
If you have a D-800, you can use a special adapter cable wired as follows:
XLR(F) pin 1 to the sleeve of the 1/8" TRS
XLR(F) pin 2 to the tip and ring of the 1/8" TRS
XLR(F) pin 3 unconnected
Be sure to carefully label this cable as it's "way not standard" and is sure to cause grief to others (or yourself) in the future if you don't.