By definition: no. But an over instrumentalisation of it would then oblige to consider humanitarian aid, even conducted by civilians, as a military actions. Then it may become a war crime by access denial. Denying humanitarian aid to access may allow war crimes to happen. Then it is a military responsibility and the whole military chain of command that has to be examined. From the private that did not let humanitarian aid enter to the Chief of the Armies and the whole government that gave the orders and signed them.
But could humanitarian actors perpetrate a war crime? The answer is the less clear. The example given by Tom of MSF redraw from Goma while 4000 people were dying per day could be interpreted as such if they were the only one present. The non assistance of ICRC to war prisoners and civilian in concentration camps during WWII could be seen as such as they were the only one to access. The too often negation of his responsibility inside ICRC nowadays is not only due to the shame that comes from his non action. At that time being anti-Semite was well accepted into Swiss high bourgeoisie and intellectual circles.
There again we are stuck in the definition of direct involvement of the chain of command.
In a "build" perspective of counter insurgency, this has to be looked at twice.
An unequal access to aid would lead to a war crime if massive number of civilians, especially "innocent" ones dies from it. The use of food and medicine embargo is still proscribed (had for Good reasons). But still we end up in the problematic of independence of humanitarian aid which, part from ICRC and MSF, is a joke.
Therefore humanitarian actors do have a responsibility, which is quite equivalent as the one of military, in distributing or not access to aid.
The ground guy executes orders from intermediate officer with the difference that he does not have the responsibility to not apply the order or redirect the aid. At the contrary of a soldier that has the responsibility to not apply illegal order.
As in the military, intermediate humanitarian officer will then deny his responsibility in putting the blame on the donors whom do have a political agenda.
But there also NGO do have, in the best case, social agendas with political goals and objectives…
Then the question is no more rhetorical and can/needs to be addressed.
Could humanitarian aid or actors being involved with direct responsibilities in a war crime?

PS: Rome Status are the best definition I have found up to now and whit which I agree 100%. Like said Abu, if we all met, we would have a 99,999% agreement on what is a war crime definition and fight with details for the pleasure of a good rhetorical talk.