Yup, the ULN2003 is used in just about every appliance I have torn down for work to drive relays. It's a great little chip and the only additional advice I'd give is that there are current limits for Darlington-arrays like the 2003A.
So review the data sheet and your LED-driving current requirements carefully to ensure that you are not exceeding the current limits of the 2003A or switch to a beefier transistor or perhaps even a electromechanical relay. It all depends on what you are trying to do - for example, dimming via PWM will not play well with most/all electromechanical relays, while simple on/off may be perfect for a relay and not so perfect for the solid state relay (heating).
You will still need a chip like a 2003A to drive a electromechanical relay, however. And, unless the chip has a built-in snubber, add a snubber diode to limit inductive kickback from the relay from damaging the 2003A.