Only (a) if you have a fixed-rate mortgage, as, in that situation, you are paying the fixed mortgage payment in money that is worth less.
But with a variable rate mortgage, banks just pump up their rates to maintain the value of mortgage repayments. Bankers don't get rich by handing out free lunches. Your mortgage is worth less to the bank (i.e. it is an asset that is being reduced in value by inflation), so they try to maintain the value by increasing mortgage rates, i.e by increasing your mortgage payments. And (b) only if your post-tax wages keep place with or exceed inflation. Otherwise you are paying more of your post-tax income to service your mortgage. And with a variable rate mortage interest rates will increase in excess of the rate of inflation, also reducing your post-tax income.
If your thesis were correct, all the advice given by numerous contributors on AAM that you should overpay or pay your mortgage early is incorrect. If you are correct the recommendation should be that, as a matter of policy, you do not pay off the mortgage early, i.e to allow inflation to reduce it in real terms and you should invest any surplus funds in the stock market, or just spend the money on enjoyment, rather than reduce the capital sum owed. It also implies that as you can't foresee future inflation with precision, but you believe inflation will reduce the value of your mortgage, you should take out the longest duration fixed-rate mortgage possible, to increase your chances of encountering a possible bout of high inflation in the future and thereby reducing your mortgage in real terms. But nobody giving this advice.....