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Yes.
You paid the card with no additional charges in the last statement cycle, paid it so the statement prints zero due on statement 1. No payment due, on what would be the standard due date 25 or so days after the statement 1 payment date.
Charge the pack of gum 5 days after the statement 1 date, and that new charge is in a new grace period, related to statement #2. The statement #2 prints 20 days later, and from that second statement date, you now have some 25 days to pay for the pack of gum. Essentially 45 days after the gum was purchased, the payment is due, on the payment date from statment #2, and no interest in this case.
If you only pay for half the stick of gum (not really an option because the minimum payment from statement 2 will handle that) and the pack of gum remains on the statement 3, then interest will start calculating from the day statement 3 prints. Interest will trigger on all new charges after the statement 3 date, because you have just carried a balance over after the Statement 3 date.