As said, RightStart does this, and Math-U-See does something similar.
IMO this is one of the greatest STRENGTHS of RS.
As an example. My daughter is only 3. She has been able to count to 10 since she was 2. Counting beyond 10 gets confusing. She usually says "eleven, twelve, thirteen, fifteen, seventeen, nineteen, twenty!!!"
But if we remind her to count the 'math way', she says "ten-one, ten-two, ten-three, ten-four, ten-five, ten-six, ten-seven, ten-eight, ten-nine.... TWO-TEN!"
Rather than it being a rote memorization of a string of words, it's a true understanding of the repeating pattern of our base-ten counting system.
She can look at an abacus, count the tens and the ones and say "that's seven-ten three!" Again, it's about understanding the concept, rather than memorizing words (most of the ten-words are just the unit-words with 'ty', but not twenty or thirty, or fifty, and forty is spelled different, and the 'teens' are said backwards, for heaven's sake... why is "sevenTEEN" such a different number than "sevenTY"???)... and it CLEARLY shows the MEANING of the numbers. 50 is five-tens by definition. Memorizing the word "fifty" as following the word "forty-nine" doesn't necessarily mean they understand the tens groupings!
As for switching over to english counting words when the time comes... I've never personally heard of a kid having problems. Kids are hearing the english words all around them all the time. They're probably very used to them (case in point, my daughter -- I've never 'taught' her the english counting words, she's encountered them in books, movies, tv shows, computer games, from friends, etc) so it's just a matter of saying "now that we understand the concepts, we're going to use the english words from now on even with our math."
And if they do resist a bit... so what? If saying "2-ten-four" helps them calculate better than "twenty-four", what's wrong with that? I can't imagine any kid continuing that into their teenage years.
We started RS with my son when he was 10 - level E. You start with the 'Transitions' lessons, which quickly goes through all the beginning stuff to ease them into the program. He learned the 'math way' of counting. Things started to click for him that he'd always struggled with before!! It was like the veils falling from his eyes!
Even after he 'graduated' back to english counting, he would still fall back on the math way on occasion, when he found himself confused by a math problem. He'd be like "forty-eight plus seventeen... argh... let's see... 4-ten 8, plus 1-ten 7... oh okay, that's 5 tens and 15, so it's 65!"
He's now 12, doing pre-algebra and the RS middle school geometry. He doesn't do the 'math counting' anymore at all, he's internalized the concept well enough now that he doesn't have to. He just instinctively understands that 48 is 4 tens and 17 is one ten, he doesn't need a cue from the language anymore. But those language cues are how he GOT there.