Err...somewhat. It's quite complex though. She's definitely quite popular considering her position but it is worth noting her polling figures are only considered to be quite decent because of where her party were before. She's still generally polling numbers lower than what Corbyn gets nationally...and he's being considered a disaster.
I'm personally from a West of Scotland constituency that's a former Labour heartland, so naturally I don't know too many Tories. And I'm relatively youngish too, which only adds to that. A 65+ year old in Dumfries, by contrast, will know many...but again, I'm not sure that's something which wasn't the case before Davidson came in. If anything she's made it mildly more acceptable to be seen as a Tory, but there's still a lot of resentment towards them as a party...and the SNP tend to poll around double their figures or above. But, as I say, I'm basically in the demographic, both geographically and age wise, least likely to vote Tory.
She's definitely seen as credible, though. Which is more than can be said for Rennie or Dugdale.