Yes, they have both reduced power draw and reduced mass. I use them on my main exploration ships and on an Adder that I keep ready for situations that require cold running (also helps to stay cool when scooping).
As I understand it the influence on heat signature will be very minor. Heat is mostly generated by powerplant and thrusters. Enhanced shields will reduce powerplant load and thus heat generation, but I wouldn't expect much from the shields alone - compare the reduction of power consumption (maybe 1 MW?) with the total power requirements of your ship. Low emissions powerplant will make a much bigger difference.
Base heat generation is directly proportional to energy usage in your ship. For non-combat ships, shields are the second biggest power hog after thrusters. So any power reduction on shields helps your base heat generation significantly. So much, that explorers tended to switch off shields when further out - before we got the warnings of 'you are not alone there'. ;-)