Arduino long distance cable tester
Sure, no reason that wouldn't work. For best results you want a known resistor of about the same resistance as, or a little below, the one you are measuring. 

However, if what you are seeing is an actual open circuit then there's little benefit to measuring the resistance - you may as well just treat it as a switch or button, give it a large pullup, and use a digital input (or even an interrupt) to give a simple "OK / ERROR" signal.