No, we won't.
I hate it when authors make you read the whole article (and look at all the ads) before answering the question posed in the title so I'm cutting to the chase and saying that no, the Dow will not hold onto 26,000 because the average Dow stock is overpriced by a fair margin, with the average p/e of a Dow stock now sitting at 23.37 vs. the historic average of 18.2. Of course the Dow is still behind the S&P (24.20) and the Nasdaq (25.75) but that's because Apple's (AAPL) outsized earnings are bringing the average down considerably.
"But Phil", you may say, "earnings we sooooo good, weren't they?" I would answer you as Einstein would and tell you everything is relative and that last year, against last year's earnings, the Dow's p/e ratio was 20.24 and now it is 23.74 against this year's earnings so you are paying 17.2% more for each Dollar of earnings than you were paying last year. That's a lot! That's stock market hyper-inflation…
As you can see from the S&P chart (I couldn't find a Dow chart), we've only paid a higher multiple than this just before the great crash of 2000 but we also paid much, much more before the 50% collapse so there may still be room to run at the top – before the inevitable happens.
Taking out Apple makes for a very ugly picture on the Dow since AAPL made $11.5Bn last quarter vs $78Bn for the other components and that means AAPL alone is 15% of the Dow's total earnings and MSFT and JPM are also around $10Bn in earnings so over 1/3 of the Dow's earnings made by just 3 companies. So, if you want to buy AAPL or JPM or MSFT and pay a good multiple – more power to you. The problem is that ETF buyers drive up the price of ALL the components when they are chasing the performance of just a few.