Overall, I'd say probably not. More recently, that's probably true. For the first twenty to thirty years, their program was highly secret, and failures were not made public. Only recently have we become aware of some of the tragic losses of the Soviet space program. Cosmonauts losses:
In space: 1+3=4 cosmonauts (during athmosphere reentering). This tragedies were well known to the Soviet public.
On earth: 1 cosmonaut (blast of pure oxygen in the prototype capsule, the same that happened to Apollo - 1 ?).
Gagarin, the first man that was in the space, died during the training flight on MIG jet.
You're talking only about cosmonauts. I'm referring to accidents or deaths involving the space program itself, which applies to the use of their technology. Keep in mind, I already noted that the more recent program of Russia has been more safe than ours.
Two launches to Mars on the 13th and 15th of October had failed while he was preparing to make a big propaganda speech at the United Nations bragging once again about the superiority of the Communist system. His appointed lackey, Field Marshal Nedelin, was told to launch a vehicle to Mars, or else. When the countdown reached zero, the huge SS-6 rocket did not ignite. Feeling the pressure from Khrushchev, Nedelin disobeyed all safety regulations concerning rocket misfires and sent the technicians out to work on the rocket. Korolev was extremely safety conscious and he argued with Nedelin about sending the engineers out to accomplish maintenance on the unstable space vehicle. In an action of bravado, Nedelin took his entire staff and some chairs to sit by the rocket as it was being inspected by the technicians. Korolev and a deputy Yangel went into a blast shelter to have a cigarette when the rocket exploded. Instantly, Nedelin, his staff, their chairs, and over 100 technicians on the rocket were incinerated in the worst accident in the history of the Soviet space program. Rather than admitting that such an event occurred, the Soviet Press claimed that Nedelin was killed in an aircraft accident.
You can find that
here.