Generally speaking, no. While it has happened in the island's recorded meteorological history, the last major storm was Allen in 1960. This is because St. Vincent is between 150 and 400 miles away from the path of most hurricanes. As a southerly windward island, it's effectively outside of "hurricane alley."
Tropical storms that later become hurricanes do pass through The Grenadines, but these are immature and, while there is a lot of rain, they simply don't yet have the destructive winds associated with hurricane season.