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Seems that way, since every result of 6 or higher is a success. So a D8 has 3/8 chance of success, exactly the same as 3D6 -- except that 3D6 could theoretically net you more than one success, while a D8 can't. I don't think I ever saw any dice result modifiers used, but 1D8-1 would be the same as 2D6 with the same stipulation.

Not exactly the same as 3d.
Just to run the base numbers without pushing.
1d6 is 1/6 of 1s
2d6 is 5/18 of 1s and 1/36 of 2s
3d6 is 25/72 of 1s, 5/72 of 2s, 1/216 of 3s
4d6 is 125/324 of 1s, 25/216 of 2s, 5/81 of 3s, and 1/1296 of 4s
5d6 is 3125/7776 of 1s, 625/3888 of 2s, 125/3888/3s, 25/7776 of 4s, and 1/7776 of 5s
Rounding to 3 significant digits Strictly speaking, 1d8 is almost 4d6...
1d10 is closer to 5d6 than 4d6
1d12 is closer

Expected results - the mean rolls. A different method of equivalency calculation
6's without push have an expected result of 0.16 successes
With push, 10/36 (assumes 1's can't push and 6s can't either so 6/36+(4/6*1/6)) for about 0.278 successes per die.
2d6 thus is 0.333 & 0.555 expected,
3d6 is 0.5 & 0.833 successes expected
4d6 is 0.666 & 1.111 successes expected
5d6 is 0.833 & 1.389 successes expected
d8 as used is 0.375 Successes per die unpushed, and 0.56 per die pushed
d10 as used is 0.6 successes per die unpushed, and 0.84 successes per die pushed
d12 as used is 0.833 successes per die pushed, and 1.11 successes per die pushed.
By this method, d12 is roughly 5d6 unpushed, or 4d6 pushed
d10 is 4d unpushed or 3d pushed
d8 is just over 2d pushed or unpushed.

In order of unpushed: 1d6 2d6 1d8 3d6 1d10 4d6 (5d6 1d12)
In order of pushed rolls: 1d6 2d6 1d8 3d6 1d10 (4d6 1d12) 5d6

The odds are different. But they are in the ballpark, and it reduces the odds of "super rolls".

I almost suggested adding a d14 and d16 (which following pattern would be 3s on a 14+)
Expected success on d14 would be 15/14 = 1.071 & 1.378 and on d16 21/16 = 1.313 & 1.641
Odds would be

weird my math tells me 34.7 to get at least a single 6 on 3D6... and still it is based on the averaging approach, my dice never work so neatly. But the more dice you roll the less control you have on the outcome as a designer.

That's correct, to get one and only one 6 on 3D6. To get at least one (which seems more relevant), it's 42%.

Obviously 43D6 is an example of taking it too far. Personally, I think anything up to 6-8 dice is very easy to parse and fun, especially if the typical roll is more like 2-4 dice.