I suppose that's a relative question. Personally, I don't think they are at all stylish, nor in keeping with the current style - I love SL pumps and the Babies boots, but the Tributes are just ugly, ugly shoes.
I am sure there are people here that will vehemently disagree with me though!
As for their popularity - I still see them in Selfridges and see people try them on, so they must have a fan base. That said, I can't remember the last time I've ever noticed anyone wearing them.
I do think visually the style isn't in keeping with current trends. Platforms haven't been "in" in a while. However, that hasn't stopped me from wanting to add to my trib collection as they are the most comfortable shoe in my wardrobe. Only slightly less comfy than my sneakers! I still see a lot of women trying them on and buying still. When they first came out, I thought they were ugly for years, but they grew on me...and then I discovered how comfy they are!
I've been seeing a lot of the tribute sandals again lately here in SoCal - not so much the pumps.
It's crazy because I last saw a ton in like '08/'09 (I think) and just recently started noticing a real resurgence of them almost out of nowhere. Works for me since my old ones are still in my closet AND they're most comfortable heeled sandals I have ever owned.
The pumps seem a bit outdated only because platforms that size are not really in right now. Though I'm sure you can probably spot girls wearing big ol' platform heels to clubs still (not necessarily the Tributes per se, just generally speaking).
The sandals I think are much more in fashion for whatever reason.