If you were doing touristy things in Kent, you are probably driving there. There's a small market in people who don't want to drive on the other side of the road but might go to Canterbury Cathedral or Dover Castle, but this is going to be pretty low level.
Or you take a coach tour. Canterbury is packed with European visitors during the summer, I'm sure many do it as an organised day trip or weekend break, and such coach tours can pick people up from their own town, rather than having to go to Lille (or Calais if trains start stopping there again) to pick up a Eurostar.
As I said, I don't expect this to be on the same level as Disneyland or as transformative as the legacy of the Elizabeth line over the past three years in terms of passenger numbers. However, the ability for Ashford to be a destination choice as opposed to just London St Pancras will certainly help in the resilience of public transport Channel crossing links, rather than just road-based ones.
From Ashford, you can be in most places by rail in Kent in 20 minutes to an hour, with the exceptions of parts of the NKML and Chatham mainline. These destinations can be easily promoted as part of a day trip for visitors coming to the UK from countries like France or Belgium.
Kent can be visited very easily without a car, and apart from Ashford or areas like Ebbsfleet/Bluewater area, which can cope with road traffic, it's certainly a lot less hassle to travel to places like Canterbury by train instead.
The level of connecting traffic between Marshlink and HS1 at Ashford will be very low, certainly not enough to drive infrastructure change on it's own. Marshlink might make a case for extending the double-track for a half-hourly service between Hastings and Rye on it's own, but the idea that hordes of people from the East Sussex coast will be travelling to Ashford for the continental train is rather optimistic
Again, I am hardly expecting hordes of people from East Sussex rushing to Ashford International for onward connections to the continent. However, Rye is very popular as a tourist attraction these days and rightly so, it's a lovely town to spend the afternoon at and can get quite busy on Saturdays.
Granted, the Marshlink is hardly a priority in terms of rail infrastructure. Personally, I think more work needs to be done on somewhere like the GWML electrification programme first than a small diesel island on the Kent/East Sussex border.
However, that's not to say if the trends show an increase in the rates of tourism at Rye from domestic and potentially in the future, International, the hourly 'diesel island' isnt a can that can be kicked down the road anymore.
Unfortunately, TrenItalia says that Ashford would be back up and running by 2029 which is still a little while away yet. However, when it does reopen, I would welcome the data and encourage the promotion of Kent tourist attractions on the continent so that the only destination isn't just London St Pancras.
A rival to Eurostar has said it would bring international trains back to Kent if it is allowed to operate.
www.kentonline.co.uk
TLDR of Source: 'Ferrovie dello Stato Italiane wishes to stop at Ashford International by at least 2029; however, Issues at Temple Mills Depot surrounding storage are the main reason no competitor to Eurostar has started running International services yet'