Lydiard's hill phase was not really meant to develop your ability to run hills. It was meant to enable you to make the transition from relatively easy paced distance runs to faster track sessions without getting injured. Neither springing nor bounding is what you'd be doing when you run up a hill during a race and neither addresses the issue you're asking about, i.e., struggling with the downhills. So I'd actually say no. And anyway, if you're a true flatlander where would you do the hill phase?
That said, one of Arthur's lesser known but quite good guys was Jeff Julian who got his best marathon, 2:14 plus, late in his career and doing nothing but distance work and then a few weeks of hill springing so you could use his example to argue yes. But Jeff was no flatlander. He lived in Auckland and his distance runs would have had plenty of hills and he never ran Boston so I don't know how he'd have fared on the downhills there.
You probably just need to discipline yourself on Boston's downhills and not get carried away running so fast that you're wrecking your legs. Someone else mentioned that maybe you could find shoes that help or change your stride though I'm very skeptical of that. It's worth a try but Boston has a reputation for being a course that some runners are just poorly suited to. I know Kenny Moore said something along those lines after he raced there.