Is it acceptable to stress the second syllable of the numbers when counting them in a row? ThirTEEN, fourTEEN...
This exemplifies a linguistic phenomenon linguist Jonathan McWhorter has brought up recently: the 'backshift' (not a technical term, he cautions, but still quite descriptive I feel!).
In a recent interview, he says:
John McWhorter: You know, the backshift is a lot of fun. Basically, when you put two words together--if you are talking about, say, a board that's black--first you are going to say, 'Well, that's a black BOARD.' But, suppose there are is some particular kind of board that's black, that is very specific and has very particular function--it becomes what we call a thing in society: suppose what you have, for example, the board that's black, that you hang on the wall, and you write on with chalk. Well, if you are going to say, 'black BOARD,' enough, because it's something so well established, then the accent shifts to the first one instead of the second one. And so you say, 'A BLACKboard.' Notice that you would never say, 'Go write that up on the black BOARD.' Or, you imagine somebody writing it on a wooden plank that is painted black. It's the black BOARD. And that shift backwards, which I call the backshift--that is not an official linguistics term, but I almost wish that linguists would [use it].
To summarize, if a compound word is just starting to be used, the emphasis follows natural speech patterns and goes at the end of the compound word. However, as usage increases, the emphasis often shifts to the first part of the compound word.
In your case, FOURteen is such a commonly used compound emphasis shifts backwards. (Note: the emphasis is still pretty slight or even neutral in most cases though; it's not as 'hard' of an emphasis as the all caps makes it sound :) )
Other examples from this interview: - 'boy SCOUTS' turned to 'BOYscouts' - 'hot DOG' => 'HOTdog' - 'cupBOARD' => 'CUPboard'
Listen to the whole segment if you have time: http://www.econtalk.org/archives/2017/08/john_mcwhorter.html
(from 42:50 to 46:35)
You can, of course, but there's no native-English-speaker reason why you would. It seems like it would make more sense to emphasize the differences between the numbers so that it's easier to keep track,
SIXteen, SEVENteen, EIGHTeen
and so on.
But if you want to do it differently, there's no rule against it. It just sounds unusual.