Can growling dogs smell me even without a purple scent ring?

Solution 1:

Even when not searching, dogs have a wider sense radius about them than humans. Unless they are asleep, it is impossible to sneak up on one undetected. However you have a small window of opportunity to sneak in and kill the dog. As I recall when sniffing you can get behind them and then walk right up to them and do the dog kill with X. The trick is to not stop approaching them, they will be momentarily distracted when they sense you, giving you a small window to keep approaching.

When they are not doing a wide sniff about in distracted mode, you can get closer before they notice you (they will notice you from behind, so you need to move in immediately for the kill).

Solution 2:

When the dog is not alerted, entering its sniff radius will distract it. Once it is distracted, however, dogs behave similarly to humans, i.e. they only see in front of them. Thus, the ideal way to deal with dogs is to distract them on the opposite side (usually with some noise) then sneak up behind them. Or you can ambush them from above of below with unlocked skills.

You can sneak up on sleeping dogs, as long as you're careful. Their wake-up radius seems a little larger than humans, but it's not at all impossible.

Like guards, dogs need a short interval to react so you can always rush it and hope it doesn't bark before you put it down.