What you have is a basic resistive current sensor circuit. It can be used to detect current draw, and if your motor has a consistent current draw when stalling, you could use it for that.
With a few caveats :-)
The motor is basically a large, switched, inductor. This means that the voltage you will see over the resistor varies as the motor turns. Hook up a scope to look at it. You may be able to fix this with a second resistor from sense point to output, and a capacitor across that output, to filter the high-frequency EMI.
The motor may also generate EMI that is higher in voltage than the 3.3V that your analog input would accept. Thus, you need some other kind of protection against over-volting the sensing input, such as a Zener diode and a small amount of resistance. Paralleling the Zener with the filter capacitor is likely to work OK.
You also need to size the resistor appropriately, both in Ohms, and in Watts. For example, if your motor draws 0.5 Amps when stalled, then your resistor will dissipate (0.5*0.5*10) = 2.5 Watts of power. A regular 1/4" resistor will probably go up in smoke after a short while with that amount of current going through it. In general, the power dissipated by a resistor is amp-squared-times-resistance.
Also, you want to make sure that the resistance is small enough that even a heavy draw from the motor won't make the voltage go too high on the output. You also don't want it to be too high so that you lose a bunch of efficiency.
A good option here might be to use a much smaller resistor (0.1 Ohm sense resistors are common, for example) and an opamp with some pre-determined gain to get the voltage to where you want to sense it with your microcontroller.
Here's an example of what a robust circuit would look like as per the above. In this case, the sensitivity is set by R3 (currently, a 48:1 amplification of the input voltage, which is 0.1V / A, so 0.5 A in will give 2.4 V out.) The opamp should be fed 3.3V and GND, too.