No, Fn+F1 does not re-enable the touchpad in my case (SVF15n190x). Repeated Fn+F1 yields repeated popup messages of "Touchpad is Off". I don't know what will re-enable the disabled touchpad, but would like to know.
I also tried additional keys at the same time as Fn+F1: Fn+F1+Ctrl, Fn+F1+Alt, Fn+F1+Windows. Same non-useful results.