Yes, but it's down to insurance being an example of an 'utmost good faith' contract: you need to disclose everything that the insurer would take into account when deciding what, if any, premium to charge. That would include what you're actually doing.
The other problem is that they tend to be 'can't do any sort of work at all' policies, not 'can't do usual job' ones.
Yes, I've looked into this a bit today and the best sort of policy has what's called "own occupation protection" which means that you're incapacitated
for the job you normally do, not just any old job.
I've also worked in insurance for many years and believe me, insurers will use any reason to not pay out that they can find. So giving them false information about your work would mean you'd just given them your premiums for X months/years and can kiss goodbye to that money.
If the premiums are excessive then it makes more sense to just have a high-interest savings plan. I will update with what I find out.
I'm going to make some anonymous enquiries tomorrow by ringing brokers and just asking straight out if they cover sex work as a profession. I suspect the main problem is that they will consider it high risk, and as a result the premiums will be high.