If those are the specific details, Yes ... you would only be able to promote that offer within that time period, as they actually state 'Cart Closes'.
Some JV offers mention a launch date and launch period/phase, for the window of opportunity for the prospective customer to take advantage of launch time pricing and bonuses, and for the affiliate to benefit from launch time contests and other incentives, but still keep the product available for sale after the launch period/phase is over ... allowing you to continue to promote it.