Yes if you put anything in the chain, it is technically no longer a DI, period. A delay will affect the signal. Realize a Delay is not a signal bypass. every delay I have ever looked at has resistors and transistors in the signal path. This will change the signal even with no repeats. Sometimes even when you bypass an effect will still change the signal, whether you can hear it or not makes no difference. The point of a DI is to get a perfect bass instrument signal right from the guitar itself with nothing else touching it. Anything you want to do can be moved, changed, tweaked, or even destroyed once it is recorded. This gives you a chance to be able re-amp, and do other things with an untouched bass guitar direct input. ANYTHING you do to the signal before it technically hits tape/pro tools/etc will change it and it will no longer be a DI. Even adding in samples technically is changing it, since you are moving it in time and this can affect the phase with the amplified signal. This is why you record it and flip the phase when mixing, again, so that you don't change the signal before it is recorded. As I mentioned before during the analog days we would just play with mic placement to help line up the DI and mic'd amp sometimes placing it closer to the speaker than you would think, but it would align the signals when they hit tape. This way you adjust the mic'd signal and not the DI.
It is no different than sticking a delay on one side of stereo guitar DI so that one take is delayed by 4ms. This changes a number of things for that take, including how it would re-amp, and yes it might make it more "stereo" sounding, but you have now affected the phase in some form or fashion as well as added something to the recorded signal. The best way to handle something like this is to record both sides (guitars) unaffected and just straight DI with the wet signals as they are. You can always bump the signals by hand in the DAW to line them up if they are having phase issues, or you can use something like the bx_shredspread plugin to change things after you have it on tape. This way if you need to re-amp something for some reason it is as it should be and you can still adjust after the fact. Anything in chain changes something sometimes even in bypass. Bass guitar is even more sensitive to phase and timing than anything else in the mix, just because of how the low end waveforms are.