My trailer has an inverter and runs my cpap machine fine. You just have to know how much current or wattage your cpap draws, and make sure that your inverter is rated high enough to handle it. I believe it should say on a label somewhere on the cpap machine how much current or wattage is required. Volts X Amps = Watts, so if you have a 1 kw inverter, you can power something that requires up to 9 amps (1000 / 110 = 9.09). If this is the battery in your truck that you need to get started in the morning, it is possible that running your cpap machine all night could run it down, so it would be handy if you knew someone who would give you a jump if you need it.
When I started using the cpap machine, I told them I did a lot of backpacking, and they said a battery powered version was available. But they also said that once my body adjusted to it, I could go a week or so without using it with no ill effects, so I haven't bothered to find out about the battery powered version yet.