The answer: A little bit, but not much. Flight director Gene Kranz (played in the movie by Ed Harris) explains:
The final ordeal of the flight was a radio silence, or blackout, caused by ionized air surrounding the command module during its superheated reentry through the atmosphere. With no radio signal, there was "no way to tell" how the crew and ship were faring, Kranz says. "There was no telemetry from Odyssey until the end of blackout," he recalls. "Take a look at the picture of the flight directors during blackout.... There was some distress, but nothing we could do about it." To make matters worse, the blackout went on longer than usual because the reentry path for Apollo 13 was longer and shallower than normal. "Per my mission log it started at 142:39 and ended at 142:45 -- a total of six minutes," Kranz relates. "Blackout was 1:27 longer than predicted... Toughest minute and a half we ever had."