Actually Barry most military historians assume the early days of 41' would've been a disaster even without the purges because the Russian Army had grown to absolutely gigantic proportions, so even had there been no purge, there still weren't enough officers to go around, the purges just made it worse, and because the older generals who weren't purged performed so poorly (being mostly hold-overs from WW1). They certainly didn't help, but given the rapid expansion of Soviet reserve forces and men under arms in general, there is no scenario for which the army would've been ready to fight at peak performance in 1941, or even 1942.
A counter-point here is the performance of the Soviet Navy in 1941. The Soviet Navy was very heavily purged in 1937 and continually purged throughout the whole period. But its performance in the early days of WW2 was exceptional. Why? Because the navy had not been expanded all that much, and the existing naval institutions could absorb and accommodate the reserves that flowed in to bring the navy up to fighting shape. The Navy was even asked to perform many tasks for which it had *never* been trained to do, and still performed in those scenarios fairly well (for example most of the Soviet Naval Air arm ended up bombing troops on land, something that wasn't really discussed in the pre-war years or the evacuation of Talinn - which was a disaster - but considering the obsolescence of the Soviet Navy and their complete lack of air coverage, it's amazing they didn't suffer even heavier losses).
I should also point out that when somebody talks about mobilization that means automatic war in these scenarios. Poland's leadership (Second Republic) is often criticized for not mobilizing earlier, but they were restricted from doing so by the French and British because Poland mobilizing its armed forces would've been a defacto declaration of war on Germany (in which Germany could argue it was not the aggressor). Germany had a distinct advantage over the USSR in having already been at war with, and conquered, Poland, Denmark, Norway, France, and Yugoslavia, in that their armed forces were already mobilized and battle tested. Stalin was very clear to *avoid* provoking the Germans if at all possible - even allowing German planes to violate Soviet air space periodically without making too much protest (by international law you could, and still can, shoot down any air craft violating your air space - the Swiss (neutral) actually shot down quite a number of German fighters and bombers during the Battle of France for violating their air space). The Red Army was on high alert throughout April and May of 1941, but after May with no real sign of invasion coming (because Operation Barbarossa had been delayed by the Italian debacle in the Balkans) they actually tamped down their readiness and alert status. It was assumed that an invader wouldn't want to contest with the rain and inclement weather that set in every year around October. They were wrong, and Germany claimed that the Soviets were secretly mobilizing and intended to attack Germany and as such their preemptive war was justified (precisely the scenario Stalin et al had sought to avoid).
Of course, Molotov in his memoirs points out that they had gotten into a kind of group think regarding war readiness with Germany in regards to May being the month - when they should've remembered that Napoleon invaded in June as well - and took Moscow. For the Red Army's part it fully disclosed (though not publicly - publicly they claimed they were invincible) that based on the German Wehrmacht's size and capabilities, and its performance against France (France was roughly equivalent to Germany in terms of men under arms, tanks, planes, etc) the USSR would need until 1943 to successfully perpetrate a war against Germany. The course of the war nearly bears that out, as the German army's victories were few and far between from 1943 on.