Your new card will have the conditions on it, at that point you don't need an ATT and they wouldn't give you an ATT while you wait on your new card, I've asked multiple times.
Let me tell you what I was told and you can make your assessment.
1) first time I asked for an ATT, I was told that the conditions are attached to my license and it's in the system. However, it was up to me whether I wanted to transport as if asked by a cop for some reason to show my license I wouldn't have the conditions nor the most recent version of my card. It would be at the cops descretion on what to do at that point. (Note that even though the card doesn't have the correct version your license is stiĺl active)
2) second time, I was told absolutely I can transport while waiting on my card. The information is in the system and the cop has all the access they have to see that you have the applicable conditions.
See link below for answers to some common questions,
http://www.rcmp-grc.gc.ca/cfp-pcaf/notice-avis-2015-09-eng.htm