Difference in sound using different carts when digitizing vinyl record?

Hello A'goners .......

I hope I am posting it in the right forum!

Here is my question - this is a hypothetical situation - if I digitize my vinyl record  while the record is played using any cart (cart #1) and then again play and digitize the same record using a different cart (cart #2), am I going to hear any sound difference typically attributed to two different carts? Everything else remain same in both cases i.e. the turntable, phono stage, DAC, preamp, amp, speakers, and all cables. The software to digitize is the same with identical setting. 

Did anyone of you do this or similar experiment? I am curious to know.

I bought a Sweetvinyl Sugarcube SC-1. I am wondering because of the conversion to A to D and then again D to A, it there a possibility that the sound differences from different carts are not so significant anymore?  Right now I do not have two carts, so can not do the experiment myself and report the results here. That is why I am asking the question and hoping to get some reasonable answers.  Please pardon my lack of technical knowledge.  

I would appreciate if we stay focused on the topic while discussing this. I do not want a debate of why I or anyone wants to convert analog to digital or one format is better sounding than the other.

Thanks and have a good day :)