It's undeniable that the purging of the Red Army's leadership seriously undermined it's capability and the Red Army would've performed better in 1941 with them alive.
It's also true that it wouldn't have made much a difference in the end.
The Red Army's biggest problem on the eve of Barbarossa was far bigger; the rapid expansion of the Red Army between 1939 and 1941. The Red Army had expanded from 2.5 million mean to 5.7 million, from 131 divisions to 316, a massive expansion as a result of the German threat. It can't be understated how negatively this impacted Soviet readiness. Already short on junior leadership, the rapid growth of the Red Army diluted what limited leadership it had. To make matters even worse, this expansion had occurred before Soviet educational reforms had time to kick in, and since conscription was utilized to fill the Soviet ranks a large number of new Red Army personnel were peasants with limited to virtually no formal education. That meant the Red Army was lacking in technicians, mechanics, radio operators, the like.
The Soviet logistical system simply coulnd't handle it, and collapsed. As a result the Red Army's forces on the eve of the invasion were lacking in virtually everything; experienced personnel, fuel, ammunition, spare parts. This more than anything contributed to the Red Army's poor performance.