Yes, researching even Militia doctrines will cause your Militia to start using fuel (not to mention taking more IC/time to build, but apparently that part is WAD). Is doctrines increasing supply/fuel consumption WAD?
A side note: upgrades increasing both IC and build time of units means that eventually the attack per IC-day you get by building a unit starts decreasing, since the number of IC-days increases quadratically, but the attack only linearly. For example, if you don't skip any upgrades, Mechanized gets less Soft Attack per IC-day in 1946 than it did in 1936! Back in HoI2 most upgrades increased IC cost only; I can understand the rationale behind both IC and time increases, but the combined effect seems a little drastic (though of course I wouldn't go so far as to skip upgrades just for that reason).
A side note: upgrades increasing both IC and build time of units means that eventually the attack per IC-day you get by building a unit starts decreasing, since the number of IC-days increases quadratically, but the attack only linearly. For example, if you don't skip any upgrades, Mechanized gets less Soft Attack per IC-day in 1946 than it did in 1936! Back in HoI2 most upgrades increased IC cost only; I can understand the rationale behind both IC and time increases, but the combined effect seems a little drastic (though of course I wouldn't go so far as to skip upgrades just for that reason).