Yes, absolutely.

Even though Tasmania is small by Australian standards, it is still a big place with relatively few people per square km (Aus is one of lowest population density countries in the world). And in Tassie the entire southwestern quarter of the state south of Strahan is still uninhabited with no roads running through it. A perfect place for a small nocturnal animal to exist undisturbed.

A couple of points of relevance:

1. I travelled around Tassie in 1999. Nearly every Tasmanian I spoke to claimed to have seen a Tiger. Now, given that alcohol was often involved and given the tourist potential for the locals if Tigers were to be found to still exist, a lot of these tales can be discounted somewhat, but I did sense that people genuinely did believe what they said and were not pulling my leg.
2. While the Tiger is closely associated with Tassie, there have also been quite a few sightings in the highlands of eastern Victoria, which is a very similar terrain and climate. Again, alcohol may be involved but the sightings are genuinely believed. My 75-year old neighbour swears up and down that he has seen one driving in the bush at night and that he was not drinking at the time.
3. It was only 2 decades ago that the Wollemi Pine was discovered. It was thought to be extinct for millions of years, but then, lo and behold, a grove of them was found 150km from Sydney. Now if something huge (25+m tall) and stationary could be sitting there rain and shine only 150km from Australia’s largest city undiscovered until 1994, then isn’t it entirely possible that a population of smallish, shy nocturnal animals could still survive in remote areas of TAS or VIC?

I am not by any means saying that Tigers DO exist, only that based on the remoteness of their supposed habitat and the large numbers of anecdotal sightings around, that the chance is definitely there, and probably a good chance at that. A wildlife biologist in TAS put the chance at “one in three” for a particular sighting (Did they see a thylacine? Footage released after 'encounter with Tassie tiger').