A carburetor that's too large will result in poor performance, particularly at lower RPMs. The engine will struggle to pull enough air through the large carburetor, leading to a lean condition, poor throttle response, and potentially even damage. You'll likely experience hesitation, poor fuel economy, and a rough idle.
While you *might* be able to get it to run, it won't run well. Unless the 350 has significant modifications (high compression, large camshaft, substantial intake and exhaust upgrades), a smaller carburetor is necessary for optimal performance.