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Without gravity, a boat wouldn't be able to float on water, so yes, gravity allows a boat to float (as well as sink into) water.

A boat floats from buoyancy force. The buoyancy force is from the volume of water it displaces with it's shape below the water. The buoyancy force is equal to the volume of water it displaces multiplied by 62.4 lbs. per cubic foot (the density of water). So if the boat displaces 20 cubic feet of water with it's hull or shape it can hold 20 x 62.4 = 1248 lbs. of self weight plus cargo. Obviously there should be a factor of safety on that.

In summary, a boat needs two things to float on water: Gravity and buoyancy force. Gravity keeps the boat on the water in the first place, but the buoyancy force is the actual thing that keeps the boat afloat. Technically, it is the buoyancy force that allows a boat to float, but if you want to get really technical, it is gravity in the first place that allows a boat to float on water.

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