If you want to do a PhD, then that's great. I hear they are a lot of fun and it could potentially be very interesting.
But I wouldn't expect that it would improve your employability as a strategy consultant - unless you went aren't happy with your undergrad (e.g., second-tier uni) in which case there might be an advantage (but only if you then got your PhD from a top-tier uni), and even then the effect is too marginal to make it worth spending 4 years doing.
In fact, many firms (except from possibly BCG/Mck) don't know how to deal with PhD's as they don't fit into their usual categories of Undergrad, MBA or experienced hire. That's probably why you are finding PhD students on this forum unsure about how to apply to consultancies.