power network consumption vs network resistance
Based on Ohm's law, \$V=I\cdot R\$, by increasing the resistance, if the voltage is fixed, the current will drop. 


Correct.


  By dropping current, the consumption or the loss will drop (\$P=V\cdot I=V^2/R=R\cdot I^2\$). 


Be careful with terminology.


Consumption implies useful work done.
Loss implies wasted energy - typically in the transmission lines or network.


Your formula shows that there is a square law at work here. At half current power is reduced to 25%.


  So, the question is: does increasing total resistance of network, result in less consumption?


Now you see that your question is ambiguous. Either way, the load presented to the power supply is less so overall consumption is reduced. Whether this is good or bad depends on where the increased resistance occurs.