But... yes. Bike can be leaned without countersteering. Though it would resemble veering off a perfectly straight line, more than steering, but it would lean.

A bike with welded handlebars will lean without problems. I've tried it!
It can not keep the leaned angle, but fall, since the bars can't be pointed into the turn, but it does lean without any countersteering - no problems. Keeping it from leaning is the problem.

If you had an on-off steering lockout switch, you could test it. Lock the bars, lean the bike, then quickly unlock the bars to be able to turn the front wheel into the turn and prevent the bike from falling. So that would be leaning and turning without countersteering.

However, like I've said, leaning without countersteering is very slow even at lower speeds.