An unequivocal yes!

IMO

Just an example, everything depends on what you actually have installed.

If your emergency heat is electric heat strips, then they may be 10,000+watts per strip (can be even higher, depends on equipment instaled). If you're electric is average priced ($0.12/kwh), then you're going to be paying $1.20 per hour to run emergency heat per strip.

For an example of normal heat pump expense, a 3-ton unit might max out around 2500 Watts. So you're essentially paying $0.30 per hour to run that unit (1/4th the cost). If you can keep yourself out of "emergency heat mode" stay out of it.