I can see how it would be a reasonable thing, if you were really dedicated to it. The battery packs I'm finding with a quick google are good for one night and you will often be without AC so you'd probably want as many packs as you expect consecutive nights without AC. And then you need stops long enough to charge all your stuff and enough outlets too. The batteries cost like $400 apiece (because medical device pricing is stupid). They weigh ~ half a pound each.
I saw a note on one of the APAP product pages about compensating for altitude. Dunno if that will mean it runs through the battery quicker.
If you have apnea as a side effect of obesity - not a dig, it's common - then it's at least possible your time on the tour will cure you of it. If you have COPD then maybe riding a bike uphill to 12,000 ft is not a good plan?
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Genesis 49:16-17