Can you expect a political Utopia when social activists actually gain control of the government they have been criticizing? That's a question probed with unrelenting incisiveness in the third episode of the memorable (so far) 26-part ''Frontline'' documentary series, In the Shadow of the Capitol (PBS, Monday, 8-9 p.m., check local listings for premiere and repeats)m. The executive producer of this consortium-produced series is David Fanning, best known for his superb work on the ''World'' series. The five-station consortium consists of WGBH, Boston; KCTS, Seattle; WNET, New York; WPBT, Miami; and WTVS, Detroit.
The ratings for the premiere of this series were the highest of any public-affairs program on PBS since ''Death of a Princess'' in 1980 - 16 percent of the TV audience in Boston, 15 percent in Chicago, 13 percent in Los Angeles, and 7 percent in New York. Fine figures for PBS, although low for commercial TV.
So unrelenting is this new show that it may make viewers feel as uncomfortable as it apparently makes its participants feel.
Reporter Charles Cobb, a SNCC (Student Non-Violent Coordinating Committee) activist in the 1960s, traces the performance of other SNCC executives who now hold top leadership positions in Washington, D.C., including the mayoralty in the person of Marion Barry, SNCC's first chairman.
The poverty and urban blight which have been afflicting more than 70 percent of the black population of Washington has apparently not been dissipated by SNCC leadership.
In fact, contemporary poverty fighters insist that when activists come into power, they are so co-opted by the establishment that it becomes impossible for them to do anything but maintain the bureaucracy. Over and over again, various black leaders make that point - a point that even the mayor has trouble rebutting.
One scene in this documentary seems disturbingly reminiscent of the recent ''underground'' film ''The Return of the Secaucus 7.'' It concerns a get-together in which 1960s activists yearn nostalgically for a return to the commitment of the early days.
Hosted by NBC's ubiquitous Jessica Savitch, who always seems to manage to pull things together and put them in proper perspective, ''In the Shadow of the Capitol'' seems to prove that, as one black activist puts it, in the long run ''politicians don't have any color.'' The idea also seems to evolve that poverty , too, has no color.
Perhaps the most disturbing conclusion is the belief of reporter Cobb that there seems to be no new generation of black activists arising in American society. In the area of social change, he believes that ''the old pressure is missing.''
The all-important question posed by this penetratingly introspective show: Will the 1960s activists be able to live up to their 1960s promises in the 1980 s? And, in any case, will the 1960s answers fit the 1980s problems?