Yes, it is possible. You will find your options for lenders a lot more limited, and that their income equivalent from your assets is much less than 4%.
Yes, it's generally better to get the mortgage and leave the rest in the market. However, you mention low income due to optimizing taxes for favorable health insurance: this is one of the rare exceptions to "don't pay off your mortgage", but you will need to run the numbers yourself. It's quite possible that in generating income to pay off the mortgage you reduce your ACA subsidy to the point that it outweighs the benefits of being invested in the market.
Other things to consider are that paying off your mortgage, while statistically likely to leave you with less money in the end, in fact has a lower chance of failure due to sequence of returns risk shortly after retirement. Finally, cash buyers are often preferred buy sellers, so being able to close quickly with an all cash offer could get you a better deal than otherwise.
While I am generally member of the "don't pay off your mortgage" club, I think in some unusual circumstances it may be better to "don't even get a mortgage".