There are many things to consider here.
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If you do an exercise too often, your body can become less and less responsive to it and improvements in muscle mass development will diminish if not stop altoghether. Even when it comes to conditioning and fat loss it will become less effective over time as you become “too efficient” at the exercise.
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Unless your daily volume is low (e.g. my “Best program for natural lifters”) you simply should not train every day or even 6 days a week. In the past I foolishly recommended such a high training frequency because I was judging what I was seeing in the elite athletes I was training, forgetting they 1) have great genetics for recovering from physical work 2) they have almost no life stress (compared to “regular people”), they had no job (besides playing sports and training) and most of them did not have families.
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While you will be able to do carries on the non-training days it will diminish your results from the rest of the program. Nowadays, even with pro athletes we train, at the most, 4 days a week.
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What is your priority? Having pleasurable experiences or getting maximum results? And there is no wrong answer here. If loaded carries give you pleasure and you enjoy doing them more than getting maximum results, by all mean do them everyday. But if you value results more, follow the plan.