But that's the whole point of A/B testing, rather than argue of hours based on intuition and anecdote you can actually test these ideas. No need for debate here, just run experiment and look at the results.
Note that debate is still needed in order to properly setup A/B test.
Only then can you reasonably discuss the issues presented. If your results say 'this is definitely a good idea for increasing purchases', then rather than do long term A/B tests it would be better to just monitor overall trends in potential abuse.
So there are really two separate issues: Do discount follow ups to abandoned carts create a large increase in purchases. This is easily answered with an A/B test
Are people likely to abuse this discount system? And how do we stop it if they do? This is hard to test with a simple A/B test and is much better answered just by monitoring the purchases and looking at the extreme cases. Also this is pretty easily solved by just adding limits to when the system grants discounts.