People no doubt escaped prisoner camps in Siberia, but they'd be less likely to succeed, or even do so from Siberia than from Alyeska.
As I understand, the
professional criminals (and definitely the political ones in the later times) had a well-established “infrastructure” supporting escapes. Judging by Gilyarovsky (a famous reporter of the late XIX - XX), the “serious” criminals had been finding their way back to Sukharevka (a “criminal district” in Moscow) numerous times with a full knowledge of the local policemen who would not arrest them unless there was an explicit order to do so. Smaller fish would, of course, have much more serious problems but then, again, Siberia of the Imperial Russia was not one big penal colony and the penal colonies usually were not in a middle of a nowhere: the prisoners had been working and result of their work had to be transported. At least some of the settlers in the area had been generally sympathetic to the prisoners and not only the Old Believers. And, of course, after reaching the ‘civilized area’ an escapee would find himself within a familiar environment and, if he was a professional criminal, he could count upon the local criminals for some help. However, it does not look like the Tsarist government considered escapes as a major or even truly significant problem.
OTOH, escape from Alaska would end up in the areas with an unknown language and culture and no “support base”. So Alaska would be more reliable but less supportable logistically and economically and as such did not make sense.