I am naturally paranoid in the world of Deus Ex, so when someone is asking me to turn off a signal jammer on the Singapore mission so they can 'track me better' my natural instinct is to leave it on. What are the consequences of leaving it on?
I don't know for sure what happens if you leave it on. My guess is that nothing bad happens.
If you turn it off, you get waypoints for the other objectives you need to finish for this mission, which makes it much easier IMO. Otherwise you're most likely left to wander around the entire map looking for them, which makes the mission much harder than it needs to be.
That said, once you find one of the objectives you can get some slightly vague pointers to the other objectives. So if you want to leave it on, you're not completely on your own, but the mission is much easier with the jammer off.