It all depends on the work being done. For most automotive cordless impacts can do just about everything an air impact can. If they can remove a Honda crank bolt, and they have demonstrated that they can, that's just about the hardest job in automotive repair. The only advantage of an air impact in automotive today is the truly compact tools like the Astro Nano Version 2 and the SPAir impacting ratchets which are very small. In any modern automotive application space is at a premium.
RedneckWelder you mentioned muck and bulldozers. Few automotive shops work on dozers or have dirt floors so that precondition doesn't apply. HOWEVER, if heavy equipment is what you do for a living there is little doubt that air is where it's at for exactly the reasons you've mentioned. HORSES FOR COURSES IS AN OLD STATEMENT BUT ENTIRELY TRUE.
While in most cases they "can" get the job done. My question is when there is air available to you is it really the best tool for the job in a production based environment?
My answer at this point is still no.
The cost overhead in the long run is still going to be higher for cordless tools when you account for longevity and batteries in most cases. Air is still needed for a lot of things in the automotive industry so you will still need a rather capable compressor unless you want another throwaway tool...
While I won't argue that cordless tools are great for most interior work and some mechanical work it will be awhile before they unseat air tools in a professional setting where air is provided.
Back to the original question of "can". Just a quick example. Can I rotate tires with my 3/8 air impact? Yes. Sould I? No. Why would I abuse my 3/8 gun and waste time when there is a easier way to get the job done?
There is nothing worse in a shop than listening to someone repeatedly hammering on something to get it apart. Whether it be with a hammer, impact or god forbid an air hammer. So when someone pulls out the cordless impact and hammers away on the "Honda crank bolt" it comes back to "can or should". My air gun will make quick work of it.
For home garages cordless is a game changer and in a lot of ways it has been for the professional but, it is not a replacement for air rather just another tool in the box.