Sgt. Drydock; The NWMP and its successors always considered themselves as military, until at least WWII. Initially the name proposed was the Northwest Mounted Rifles, and early uniforms were rifle-green. It was changed to "police" for fear of offending our kindly neighbours to the South.
Artillery was included in their establishment from the beginning. A 9 Pounder was used during the Riel Rebellion in Saskatchewan in 1885. In 1897, a 7 Pounder mountain gun was used during the 3-day siege resulting in the death of Almighty Voice.
Machine guns, Maxim and Nordenfeldt, were deployed in the Klondike, 1898 to 1900, and held in stores much longer. Lewis guns were acquired during WWI, and only handed over to the Army in WWII. Machine guns were deployed on riot duty in Winnipeg in 1919, and in Saskatchewan in 1931 during a penitentary riot, and 1935, to halt the "On To Ottawa" trek.
For the Boer War, the NWMP provided the cadres forming two or three Mounted Rifle contingents, Strathcona's Horse, The Royal Canadian Dragoons, and the Canadian Mounted rifles. I say 2 or 3 contingents, as Strathcona's Horse, commanded by Sam Steele, was an Imperial regiment raised in Canada. Both the Straths and the RCD are armoured regiments in Canada's regular army.
During WWI and later during the intervention in Russia, the RNWMP provided two cavalry squadrons.
It might be debated, but the mounties had long considered themselves as military. So, why shouldn't the NWMP carbine be considered for the military class?