The answer to this is "No". The T-34 was produced at the following Soviet factories in the following numbers, although as with any Soviet statistics, these are more estimates that absolutes, and there are higher numbers given which likely also include full-overhauls rather than just new production.
| Factory | Production |
|---|---|
| UZTM | 719 |
| CzKZ | 5,094 |
| Zawod No. 174 | 5,867 |
| STZ | 3,770 |
| Zawod No.112 | 12,604 |
| ChTZ No. 183 | 1,675 |
| UTZ No. 183 | 28,952 |
| Total | 58,681 |
The closest thing that can be said about American "production" is that the T-34 was based off of the Christie suspension design, an American design which they had initially copied wholesale with the BT-2, a copy of the Christie. To be sure, America (and the UK) was building tanks for the USSR, but rather than going through the process of retooling for production of Soviet designs (assuming the Soviets would even have agreed to it), they were sending their own designs.
| Type | Delivered |
|---|---|
| Matilda II | 918 |
| Valentine | 3,332 |
| Churchill | 263 |
| Cromwell | 6 |
| Tetrarch | 20 |
| M3 Stuart | 1,232 |
| M5A1 Stuart | 5 |
| M24 Chafee | 2 |
| M3 Lee | 976 |
| M4A2 Sherman | 3,664 |
| M26 Pershing | 1 |
| M10 3in GMC | 52 |
| M18 76mm GMC | 5 |
| T48 57mm GMC | 650 |
| M31 ARV | 127 |
| Total | 11,253 |
T-34: Mythical Weapon by Robert Michulec
Soviet Lend-Lease Tanks of World War II by Steven J. Zaloga