It's a good idea. You can always try it out and if it's doesn't work, bring it back. I suppose if you brought extra batteries you could use an bring and use an impact wrench and a portable vacuum too.
What I don't know is that the CFM will fill the tires very quickly and you might run out of battery after a set of 4 tires? Plus if it's a multi day trip you will need to bring a charger with you.
This is just guess work math so take it with a grain of salt. To put in perspective this HF compressor claims 3.5 Mins for one tire,with a bit less than 1CFM, they don't state beginning and ending PSI. Let's assume it's near 0 PSI to 30 PSI.
12V 100 PSI High Volume Air Inflator
You can bet that their number is a small tire like 185/65R14. Your ~32" tire on 16" rim is about 77% more volume and will take about 6-7 mins each. We know that HF lies about the specs so let give it a 20% margin. It still puts you in the 20 min range for 4 tires. With fresh batteries it could work, but once they wear down it might be a bit tight.
Oh, BTW the higher the working pressure the less the CFM. So if you want 40 PSI you might as well break out a beer and take a break.
I use a home made CO2 tank with a back up 12V compressor. You can make your own basic "power tank" for about $100. If you want more goodies just add them on. It will fill a bunch of tires way faster than any air compressor will and you can run air tools off it.
Check this out.
https://www.youtube.com/watch?v=n5lyJ_IzJ9E
Please post back and tell us what you figure out or decide?