By crit/miss, I mean literally the stuff in d20 that needs a natural 20 (or a natural 1).Hmmm. Two thoughts:
(1) Generally the complaints people have about d20 are precisely about those crit hit/miss zones, especially something that should require a crit success for a beginner but is straightforward for an expert, like navigating rapids or climbing a reverse-slope cliff.
If you scale modifiers (and DCs) as described, you end up with within a few % of the same chance of success/failure with 3d6 vs 1d10 as your core random number generator.
Only in the cases when the d20 only fails on a 1, or succeeds on a 20, does the 3d6 provide additional resolution. But its difficulty for the expert is unchanged; what happens is, 3d6 breaks the "natural 20 to succeed" into "6%, 4%, 2%, 0.5%"-ish steps.
This is similar to saying "natural 20 isn't an auto-success; if you roll a 20, you can add an extra 1d6 to your roll". That is what I'm saying "outside of critical hit/miss mechanics", the rescale of modifiers with 3d6 results in an almost impossible to distinguish success resolution engine compared to using the d20.
When people talk about using 3d6, they do not usually focus on the changes in crit/miss chancesin my experience. If they do talk about it, they talk about working to ensure that the chance is the same or similar with 3d6 as with 1d20, which tells me any difference isn't their goal.
Of course, if I successfully teach people that is the difference, people will claim it is why they wanted it all along. That is an inevitable part of analysing a game system someone wants to use.
The margin of success is just scaled.(2) Dungeon Fantasy/GURPS gets extra mileage out of the 3d6 bell curve by utilizing margin of success (either directly or via Quick Contests, e.g. for a feint, or resisting a spell). Since the bulk of the probability curve will always be around 9-12, each extra +1 not only boosts your success rate but boosts your average success margin. I don't know whether or not that makes GURPS not strictly "roll over/under" by your definitions, but it does suggest that merely shifting D&D to a 3d6 bell curve without utilizing margins of success will not yield the same benefits you get from Dungeon Fantasy/GURPS.
Thank you especially for insight #2.
Unless the exact amount of margin of success matters significantly more than the actual success, nope.
But, imagine a game where you rolled d20+modifier and what mattered was getting exactly 3 away from 15. Not within 3, not 3 or more higher, but your goal is to be exactly 3 away. That is a case where 3d6's bell curve isn't integrated and smoothed into being nearly the same as a black line.
It isn't a mechanic I'm aware of used in RPGs.
An actual example of a RNG that isn't roll over/under is Greg Stolz's ORE's "find matching pairs of dice from your pool of d10s".