Is the Induced EMF additive to the circuit?
Your top diagram doesn't make much sense.  However, if you have a closed loop of a power supply and resistor as you show, then the EMF induced by a changing magnetic field enclosed by the loop will add or subract from the power supply voltage, depending on the polarity of the magnetic field change.

You can actually wire this up and see it.  Make a circuit of a power, supply, resistor, and the secondary of a transformer, all in series.  Assuming the transformer secondary DC resistance is small compared to the resistor, it's effectively not there as long as the primary of the transformer is not driven.  When the primary is driven, there will be a corresponding AC voltage induced across the secondary.  This secondary is in series with the supply, so the resistor will "see" this voltage plus the supply's voltage at any instance.  Note that overall, the transformer will only put out AC, so at times it will add to the supply and at other times subtract from it.

For example, let's say you have a 7 V supply in series with a transformer secondary that puts out 1 V peak AC sine.  The resistor will see the voltage varying sinusoidally between 6 V and 8 V.