Are morning headaches caused by sleep apnea consistent?

There is a lot of variance between people who have sleep apnea, whether it's symptoms or how/what type of treatment works for them. I'm afraid it's a sometimes lonely journey of discovery, although it needn't be if the individual is willing to learn and to inculcate experiences as expressed by other sufferers.

Generally, if you would rather live, including living better, you must have treatment for sleep apnea if it is formally diagnosed (best done in an over night sleep lab, a process called a polysomnography). From there, a qualified respiratory therapist or some other physician/sleep expert should prescribe a treatment, almost always with a CPAP/VPAP/ASV machine (CPAP is continuous pressure, VPAP is variable pressure, ASV is an adaptive servo-ventilator used most commonly to treat central apnea or mixed/complex apnea).

Your headaches might be from another cause, but if you are not being treated properly (you have the wrong machine, it's not set properly, or your treatment needs to be reviewed because of a change in your circumstances), you should expect to have problems.

@gloaming has excellent advice.

When my sleep apnea was undiagnosed, I had constant headaches. I was taking aspirin three at a time, several times a day, every day.

Even after getting a CPAP, I had periodic, intense headaches, but that may have been my job, my commute, my poor diet, or any one of a number of other causes. Maybe even restricted blood flow to my brain that led to a stroke in 2018. Who knows?

But there are a lot of possibilities here, so you should probably see a professional to narrow down the cause.