Q: Would a rear brake caliper that was siezed cause the ABS light to come on?

ABS is capable of monitoring differentials in wheel speeds, and rates of deceleration, and there is no way the ABS system could "know" whether the brakes are in good repair or not. However, if the caliper was seized such that the rotor was impeded from turning at the same speed as the other 3 wheels, that could set up a circumstance for an error code. Inasmuch as the ABS codes that have set on your vehicle can be downloaded, whatever the actual, in fact, fault is with the ABS system, including the cause of the ABS malfunction(s) will be "within", or suggested by, the trouble codes that have been set. The most efficient thing to do to restore the ABS system is get an ABS light is on diagnostic which diagnostic will identify the faulty component, including sometimes just a wiring fault. Getting back to the stuck caliper and all possibilities, though, if corrosion caused the caliper to seize you also have to consider the possibility that the ABS tone ring, or reluctor, in that wheel position has enough foreign material on it (rust, etc.) that a code could set. But, again, if that problem existed, that and all other "causes" would be revealed in the downloadable ABS fault codes in all events. Really, the key is to download and follow up on those ABS codes because that will resolve the issue for you. Please let us know if you have further concerns and I hope we can resolve this for you.