Yes, if this sensor goes bad, it'll give the module(brain) a bad signal and could cause the ABS to act, when it really shouldn't.
I worked for Ford/Lincoln for 20 years and during that time, I had many Town Cars around that year exhibit a microscopic corrosion problem. I found it by accident years ago and maybe a great way to save a hundred bucks or so.
Try this: Disconnect both front ABS sensors under the hood and spray inside connectors with electrical contact cleaner(brake cleaner works also) and blow out good with compressed air. Squirt some dielectric grease into connectors. Grease will ooze out when connecting, as this is normal and assures a watertight seal.
I've fixed a couple hundred Town Cars with this procedure will " 0" comebacks. If the sensor is bad, this won't help at all, but maybe worth a shot!