No. Wild turkeys (Meleagris gallopavo) feed on the ground, which might explain the myth of their flightlessness. They can in fact soar for short bursts at up to 55 mph.
But their tendency to stay on or near the ground contributed to successful hunting that brought the wild population of turkeys down to about 30,000 in the 1930s. There are now 7 million of them.
The myth of turkeys' inability to fly may stem from the fact that many domestic turkeys, such as the broad-breasted white turkey — which is the most widely used breed commercially — cannot fly; they are too weighed down by their own meat.
These birds have been selectively bred to be much heavier and possess a larger, broader breast, the weight of which keeps them perpetually grounded.
You can learn more facts about turkeys here.