Here is the short version. Most standard comprehensive car insurance treats putting the wrong fuel in as driver error, not an accident, so plenty of policies simply do not cover it. Some do, either as accidental damage or a specific misfuelling benefit. The only way to know for sure is to read your policy's product disclosure statement, or ring your insurer and ask.
Even when it is covered, there is usually an excess to pay, and on most policies that excess is around the same as a straightforward drain, sometimes more. A claim can also affect your no claim rating next year. So for a simple wrong fuel drain, a lot of people are better off just paying for the job and skipping the claim altogether.
Roadside cover like RAA is a bit different. It generally will not drain your tank, but depending on your membership it may tow you home or to a workshop. If you would rather go that way, get towed home and we will come and do the drain and flush there, no problem. Either way, the car gets sorted.
The one thing worth knowing: the big bills come from driving on the wrong fuel, not from it sitting in the tank, and that damage is the hardest of all to get an insurer to pay for. Draining it early, before you drive, is the cheap and certain path. Whatever you decide on the insurance side, sort the car first. See our petrol in a diesel and diesel in a petrol pages for the mechanical detail.