Let's clarify the question, first of all:
Can Australian Cattle Dogs be left alone all day in an apartment?
Short answer: NOOOOOOOO!
Can Australian Cattle Dogs live in an apartment?
Short answer: All heelers need a lot of stimulation, interaction, and exercise. If you can provide this, a heeler is perfectly suited for an apartment.
The long answer:
Well, of course they can!
The standard "literature" published on Australian Cattle Dogs suggests that no one should ever have a heeler in an apartment. Ever.
It doesn't matter what type of housing you have. What DOES matter is that they get exercise and mental stimulation. I live in a house with a yard and you know what, we STILL had issues with our young heeler [literally] chewing the walls from boredom. While ample space for running around outside, without interaction and a "task," he really doesn't care to. Given the choice, he'd much rather chew the drawstrings off of every pair of lounge pants.
A more important consideration than space is time and dedication; someone in an apartment who is willing and able to learn, train, exercise and interact is infinitely more well suited to have a heeler as a household pet than someone with a large yard and no time or interest in the animal as an individual.
That all said, heelers DO need a lot of actual, physical exercise. As my partner and I both work, we depend on some outside help for this during the week. Two solutions we have found work well for our little household are dog parks and doggy day care.
These work really well are because there are other dogs there.
While you can hike and trek and throw the ball for hours at a time, nothing will wear out an energetic dog like another dog. You can't run as fast (sorry to break it to you), you can't grapple with your face in 10 minutes bouts (I mean, you could, but ouch), we can't run from one to another sniffing the private bits (again, you, um, COULD, but...) Any opportunity you have to get your heeler with another dog - do it.
A cool trend we see happening in the city is high-end apartment buildings utililizing the market interest for pet-friendly amenities, like on-site dog parks, so if you're still in the exploratory phase of adopting a new family member, check out what's happening in your area.
An option I haven't personally pursued is a dog walker. Apps have made hiring dog-walking services super affordable and easy.
You can also make an effort to allow for your day-to-day activities to include your heeler as much as possible; instead of going out to dinner, have a picnic at a park. If you do go out, check around for patio dining that allows dogs (pro tip - microbreweries tend to be very dog-friendly). If you're working from home, take your conference calls on a walk. In fact, walk as many errands with your buddy as you can.
To summarize, all heelers need a lot of stimulation, interaction, and exercise. If you can provide this, your heeler will be perfectly suited for an apartment.
"A tired heeler is a good heeler."