I don't think so.
If her coming is what I think is important, then we have a choice between:
1. It is important that she comes
2. It is important that she should come.
(I have a feeling that Americans might say, as an alternative to : It is important that she come. Can any Americans among you confirm (or reject) my feeling that you use a subjunctive?).
I don't feel a great difference between  and . In  should has no more suggestion of obligation than it does in :
3. If I should die, think only this of me ... in neither  nor  is ought to appropriate
I tell my students that whenever we use ought to we can use should, but the reverse is not true. This is because, ought to, unlike should, always has some idea of obligation/duty/necessity. This idea can be a logical necessity as in:
4. He left 3 hours ago, so he ought to be there by now.
In  and  there is no sense of obligation, and therefore ought to is not possible, as we noted above. The same is true of your example (, below).
5. It's important that she ought to come in time.
If you said that, it would appear to suggest that what is important is the necessity for her to come on time.
Student or Learner