Do you need to run the General Test under 401(a)(4) for an Age Weighted profit sharing plan?

yes

Maybe not. If the design is consistent with 401a4 assumptions, and there is nobody who is beyond retirement age, the plan will, by definition, pass the test. So there is no need to run it. However, if you aren't sure that you don't need to run it, by definition you will not know that the assumptions are necessarily consistent with 401a4 assumptions and, therefore, it is probably better for everybody if you do run the test.

Of course, this assumes that coverage satisfies 410(b), too.

the other unusual circumstance that could cause the plan to fail would be to have young non-key HCEs who receive a top-heavy minimum rather than the contribution through the age-weighted formula.