Yes, always. I think the real essence of refactoring is picking which steps to start with.
I find the thing with refactoring large changes in a safe manner is always to have a reasonably clear picture of where you want to go. Then consider your existing system and try to find out which pieces you can introduce that have least likelyhood of being a radical change. Then you can introduce these in a controlled and well tested manner.
So what you do is to work in the vincinity of the nastiness. Not always attacking directly from the front, but sometimes just chipping away small pieces. Usually I wait, and only go for the "big prize" after a few rounds of chipping away at minor nastiness. But I know where I want to go.
The nice thing about working this way is that you can maintain progress. You never "stop development to do refactoring". Arguably there are cases where stopping is the correct situation, but most of the time it's not.
The idea here is that if you "start" with cashing in the prize money, you will be spending the next X days doing the drudgery. And there's risk, maybe you chicken out or it doesn't work - or spend 6 months instead of a week. If you do the drudgery first, cashing in the prize will be possible with less risk. And your code will improve as you go. Sometimes you can decide that doing half the job was enough, since your understanding of the problem increases. Sometimes your idea of where you wanted to go was slightly botched, and you can realign your goal as you progress.
But its tempting to go straight for the reward.