Yes as since the running of HS1 to North Kent a fair amount of people have been using it to access Stratford and St Pancras directly, and these trains do have a following as they can get quite packed and many people do get out in the places hs1 has created for them. If you look at a station from Faversham to Rochester you will see that though many might get on the Chatham mainline, some on the Thameslink via luton, still a lot of people get on the Javelin service as there is a lot of demand for it still despite having those 2 London bound services already there.
There is demand from North Kent to East London as it means that the GEML is a short walk away without needing the Tube for Startford and For St Pancras we all know there are 3 terminus stations in short distance of each other (St Pancras itself, Kings X and Euston), Many use Stratford for West Ham games up there, Despite Kent having a couple of large shopping outlets some go to Westfields in London, some mentally prefer it over the slow crawl out of Victoria as it feels like its actually going somewhere rather than a painful stop start train before its even reached the Kent border, and there is the straightforward answer of commuting.
From the London point of view many like the idea of the Kent coast being in easy access, the Medway campus hosts 3 universities, and you have got general attractions such as for example Rochester.