Is this usage of an Op Amp valid?
The basic idea should work. Here are some things you'll have to deal with.

First, the op amp's output voltage should be measured between the output and ground, not the output and the inverting input. That's how the Arduino will measure it. (Unless the Arduino's ADC has a differential input?)

Second, the gain of a non-inverting amplifier is the ratio of the feedback resistors plus one. So your gain will be 101, not 100. This is currently hidden by the incorrect output voltage measurement. Not a big deal, necessarily, but your software will need to account for it.

Third, you'll probably want a "rail-to-rail" op amp. An op amp's output can only get so close to the supply rails. (How close? Check the datasheet.) At low currents, your output could bottom out well above 0V. You also need to think about the high end. You probably don't want to target exactly 5V for the peak output, since that risks clipping on the ADC input.