YES, you can power a CPAP machine with your device.
HULKMAN jump starters are set 12V DC output port, so you can use the cigarette lighter adapter to power the CAPA. However, before using it to power your device, please fully charge the jump starter for a longer use time.
However, your own devices sometimes may fail to be powered:
You'll see a charging error on your own charging devices, when using the 12V DC output port with your fully charged HULKMAN Alpha jump starter.
When the HULKMAN Alpha jump starter is fully charged, the output voltage of the jump starter would be higher than 15V, sometimes even higher than 16V. When your own charging device detects the input voltage is higher than 15V, it will trigger a built-in over-voltage protection automatically, which may cause your own devices fail to be powered
Therefore, if your own devices fail to be powered, please avoid powering your device with a fully charged jump starter when using the 12V DC output port.