Absolutely. Lots of migrants, however, also come to Greece all the time and can't move on. Nobody seems to know the actual numbers, although the incoming flow has reduced after the EU migrant deal with Turkey.

The mechanism works e.g. so that a family runs a tourist hotel on an island; plenty of migrants arrive and there is a camp next to the hotel; tourists feel that the holiday environment at this hotel isn't nice and they no longer come; the family is without work and emigrates to Germany to work there. And also the people who supplied food, cleaning services etc to the hotel are out of work and emigrate.

The family is not racist, they help the needy migrants that arrive on their shores, but they lose their livelihood and have to become migrants themselves.

The situation may now be helped by souring EU-Turkey relations. There are not many tourists from Germany going to Turkey any more. Therefore the tourist industry in Greece could recover.

Is there any data to support the idea that tourism collapses due to a negative effect on the holiday environment caused by emigrants ...? How was tourism doing during the height of grexit (and before immigration became the global problem du jour ...)

Based on the number of tourist areas that depend on/benefit from cheap labor -- there's not a lot of me that believes this is a real mechanism...

I've just seen what some Greeks wrote about losing their livelihood and then emigrating, but recent statistics are hard to come by. I would think that the overall tourism in Greece is alive and well (particularly with EU tourism to competing Turkey collapsing due to Erdogan's arbitrary and autocratic appearances) but the Aegean islands affected by migration have suffered and people who lived and worked there go elsewhere.