Unfortunately, no.

The idea behind the BT series of tanks was breakthrough exploitation. After the enemy defenses were penetrated (more likely by T-28 and T-26 tanks) the BT tanks would then penetrate deep into enemy territory where there were no anti-tank defenses, smashing their supply lines and headquarters. In this function, speed was of utmost importance.

Technically, the tanks were capable of making these long penetrations. Experience in the Polish campaign showed that BT tanks could make long and rapid marches required in this kind of action. However, even in the nearly unopposed campaign the tanks only kept moving due to captured fuel supplies, as the Red Army's supply lines could not keep up with them. The same issue came up in the strategic operations of 1944 and 1945, but in 1939 there was no solution to it yet.

In 1941 there was a slightly different problem. The fuel that tank units were issued was not physically stored at the units' location. It was merely allocated and kept in a central storage facility. Due to the surprise nature of the invasion there was simply not enough fuel available for these kinds of attacks or enough fuel trucks to deliver it to the tanks.

Furthermore, there was another issue. In order to fully take advantage of the tank's speed you need to know where you're going. The situation in the early weeks of the war was pure chaos. Information regarding the enemy's location was sparse and vague. Tank units wasted their time and resources dashing back and forth, often on contradictory or confusing orders. The front line was theoretically fluid enough for an exploitation style attack to be made, but it would almost certainly end in encirclement and destruction since there was no way to support it.

Of course, BT tanks were still used in large numbers, but far from the way that they were envisioned initially. The way these tanks were used was no different from that of the Red Army's other tanks, and even the homogeneous BT tank units quickly fell apart. Towards the end of the summer of 1941 you see BT tanks fighting even in the same platoon as T-26, T-34, or any other kind of tank without any doctrinal distinction on how they were applied. It's possible, of course, that the tanks' speed made a difference on the tactical level, but not a strategic one.

http://www.tankarchives.ca/2013/10/bt-7s-in-poland.html

http://www.tankarchives.ca/2015/07/common-questions-red-army-afvs-in.html

Robert Forczyk Tank Warfare on the Eastern Front, 1941-1942: Schwerpunkt

M. Postnikov Bronezaschita Srednikh Tankov T-34