In short: Yes they do.
The Sugarcubes were a hit back home and a fresh wind for the whole music scene, way back then - so the group did become a house hold name (Sykurmolarnir) and the most popular songs are still played on the radio.
Glíngló is one of Iceland's most sold albums ever and is still selling good ...personally I do like it a lot! Somehow it fits Björk to sing the Jazz.
Frankly, I don't really know about how much Icelanders like Björk's solo career (since I haven't really been living in Iceland since that time) - personally I am not able to connect to her work - it's just not my thing ...though I like her differentness ...but it's becoming a little bit 'the same' lately ...I guess.
You know, she was already singing at the age of 12 or so and had a hit album when I was around 11 - and I hated it, he he! :)
I guess that if you have heard that voice since 1980, you get a little cranky when it follows you to other countries ;-)
I must say that I do connect more with her when she sings in Icelandic - makes sense I guess.
--= ON TOPIC =--
Björk once said in an interview, when asked about the weekend drinking habits of Icelanders: Why bother to drink during the week when you can down a bottle of vodka on a Saturday night!
....I guess we now call that binge drinking :) Mind you! This was before beer was legal in Iceland (1.March 1988).