They will easily rise above Widener, but fail to achieve parity with Temple, Rutgers, and Villanova, at least in the immediate few decades.
Drexel will ultimately rise above Widener because of its location near the center of the Philadelphia legal job market. It is easier for Philly firms to interview at Drexel, and easier for Drexel students to interview at regional firms. This will ultimately draw away students at the top of Widener's LSAT/GPA range who couldn't get into Temple, Rutgers or Villanova.
Temple will stay ahead due to its relatively low cost combined with its established alumni network. Villanova will win over those who want its alumni network and don't want to go to school in West or North Philly and likewise retain its position. Rutgers will continue to attract NJ residents looking for a tuition break.
As the decades pass and Drexel builds its alumni network, it can probably make gains on Villanova. Unless it can reduce tuition substantially, students looking for a bargain will almost certainly continue to go to Temple and Rutgers.
The biggest hurdle for Drexel making gains in the ranking game will be the USNWR reputation rankings. Few biglaw hiring partners or judges will know much if anything about Drexel's law program, which will result in low scores.
It is extremely difficult for a new school to rise in the rankings. Consider also that Drexel's competition is not sitting still - they will continue to aggressively recruit new faculty and better students.
Ultimately, I don't think it matters much whether Drexel ever rises above T3. The Drexel name is generally well known in the region and Drexel does not have to fight historical stigma like Widener does.