Sadly not where I live.
My dog was 8/9 weeks old and rehomed in the UK (my daughter dealt with all of this) seven and a half years ago. I've posted about this on here before, actually, but even at such a young age, it was very evident that she'd been abused - essentially, she's neurotic, hates men, won't allow anyone near her head, and is very possessive over certain things/people. Anyway. She is a Kokoni - which is a pedigree breed in Greece, but translates to "street dog" or "mixed breed". I spent time on the Greek islands as a teenager, and remember seeing these dogs with terrier heads and Pekinese tails running in packs through the streets...
Two years or so later, suddenly there's an influx of middle-class "naice things only" families (including my son's best friend's) adopting three years plus Kokonis, from (I assume) the rescue pages for them on FB... They were boasting to all and sundry how much 'Clara's passport had cost, I don't remember a quarantine period being mentioned (is that not a thing if the animal has its jabs and a passport?),just "oh, aren't we fabulous, we're rescuing a street dog from Cyprus!"- and I remember politely mentioning how many dogs there are in the UK needing homes. But I suspect the meaning was lost on them.
In a square mile of my home, there are 15 Kokonis (not including mine) who have been rescued by people who chose SM kudos over a dog from Battersea, say. All of these dogs (and I know this, because I belong to the local Kokoni "club" on SM) were 3 years + when they were adopted. Their owners boast about them being both rescued and Kokonis (I say mine's a rescue, because if nothing else, we rescued each other, and that she's a mix of breeds... because she is) and look smugly down their noses at the other dogs who were clearly sourced from a breeder... What they're not saying is that not one of these dogs understood English when they arrived (why would they?), none were even slightly trained, and they were obviously there because a lot of the families had kids under 8, and they were a way of circumnavigating the system. Thy wanted a dog, they wanted to rescue (great!), but they had young children/grandchildren... let's go through one of the dubious rescues on FB...!!!
My son took my dog over the road to visit 'Clara' once - only to have his best friend's mother stare at our pup in astonishment because she understands English, does as she's asked (?told), and very obviously was protective of "her boy". Snobby woman who was bewildered that we lived on the council estate over the road, wound up rehoming their poor dog into Battersea (ironically) after two years because they couldn't cope with the trauma that the poor dog had clearly endured... Meanwhile, as I'm typing this, my deranged mutt is curled up with the kitten she thinks is her "baby", next to me on my bed, snoring her contented little head off. I do wonder if she requested the "puppy playdate" (my son almost laughed himself sick when he said that's how best friend's mother had phrased the invite for our dog to visit theirs) in an effort to make herself feel that she was better than "the woman from the council estate" with "these dogs". Whilst a rescue, my dog's been with me for her whole life bar two months. I trained my first dog when I was 3 (my mother bred and showed GSDs - I had a little mixed breed). I will never bring a traumatised dog from another country into my home, when there are so fucking many in UK rescue centres that need rehoming. My son came home and said that my dog had behaved beautifully... and she was never invited back! (We do meet up with a couple of the better behaved owners and their Greek rescues from the local SM group every once in a while, though, because we like them...)
Every single rescue dog from Greece or Romania is, I guarantee you, introduced with their country of origin as the introduction - because of the snob factor in it. A common or garden Battersea rescue dog isn't good enough for them... or they know they wouldn't meet the criteria for one!
So, yes; round my way... the rescue dog from Greece/Romania (mixed breed dogs at that!) is very much a thing. Sadly.