No. The BTU is a unit of energy. A N-m/h is a unit of power. They are incompatible.
A newton-meter is also called a joule, and is a unit of energy. There are at least five definitions of the BTU depending on the starting and ending temperatures of the water; however, the most common has the relationship
is 1 BTU = 1.05506 kJ. This BTU is usually denoted by an IT subscript and was defined by the 5th International Conference on the Properties of Steam, ie it comes from international steam tables. Other definitions vary by a few tenths of 1%.
You need to know the heat content of the gas per unit volume or mass. For example propane has about 2.5X the heat content of methane. Natural gas is mostly methane, but trace gases can cause the heat content to vary 10% or more. So the conversion will depend on gas composition.
Once you do that, you can convert the volume to other units, or, with density, convert mass to volume.