It is certainly true that the 120 volt outlets in your TT are only powered when plugged into shore power or plugged into a generator. But as others have mentioned, it is possible to add an inverter (be careful, get one of the more expensive pure sine wave inverters, as some devices do not work well on the cheaper modified sine wave inverters) to power a 120 volt AC CPAP. An even better choice would be a 12 volt CPAP. This still leaves you with the problem of charging your batteries, of course.
Generators have two disadvantages, noise and toxic exhaust, making them undesirable overnight and fuel costs/maintenance. Solar has much to recommend it in comparison, with the primary disadvantage being that you need enough batteries to carry overnight. As always, you pays your money and takes your choice.
For what it's worth, I noted a coupon in the last couple months' Harbor Freight mailers (probably available also in one of the in-store handouts) for a 100 watt portable solar kit complete with charge controller, normally $189, with coupon, $149. Such a kit might be able to keep your battery charged under the right circumstances, and would certainly be cheap enough to give you an education on the use of solar.
Clicky, to the kit, but no coupon.