I did the numbers with the AT&T sales rep here in South Texas, which has a similar plan and cap. If my math is anywhere close to correct (questionable), actually pulling 1000 Mbps would would exhaust the 1 TB cap in about 2.3 hours.
Yes, hours. That cap cannot sustain the advertised speed for even one full day before hitting overage charges.
Needless to say, we went with a different service provider. We are fortunate here to have an option (alas, still a cable company) that has no data cap, but not everyone is so lucky.