Very unlikely. At an estimate, my average price is around 10K. The bulk of the coins I bought (I am guessing 85%-90% of my current holdings) were priced in the 3-15K range - after that just smaller incremental purchases over time, on a monthly basis.
Same will be the case for anyone who who starts with zero and buys now, building up to 1 BTC over say the next year. When BTC hits 1m, all the little variances between 850K and 1,000,000 won't change the fact that they are way "in the money", no matter what the price.
If maintaining the lowest possible average buying price was your concern, then of course you would never buy after you initial buys, if you were an earlier adopter such as myself. However, everything I am buying at 85K, will be 10x at 850K. So, not as much of a gain as what I bought at 8.5K (which will be a 100x gain at 850K). But the past is the past, and any gain over and above the rate of the devaluation of the USD is something I will be happy with.