Depends on the radial thickness of the tool's teeth, of course. If they are as thick as the typical original tool (in my picture), then of course they would still clash. But if they are only as thick as the radial depth of the spline in the lockring, they wouldn't not clash. Note that the lockring itself (even when fully tightened) does not clash with the adapter. There's still a gap.

Basically, a lockring tool with slightly larger inner diameter would already solve the problem. Whether that would completely erase the webbing between the teeth or just make it thinner - doesn't matter,