Can you insert a dummy task in a critical path?

No theoretical reason why you can't, but there must be a good reason to do it, as the critical path is what you need to concentrate on to get the project completed, as extending the duration of a project is not normally a good thing to do. Adding dummy tasks into a schedule is a dangerous thing to do, especially on the critical path and if they are not clearly marked, not resourced or not costs. The only reasons I can think of putting a dummy task in, is to:

1. Show when resources assigned to your project are available when you are not using them (waiting time) so they can be used on other projects;

2. Showing when you could undertake other tasks not related to the project (e.g. take project related additional 'nice to have' training, take holidays etc);

3. Making some kind of contingency visible on the schedule.

You need to have a good justification on why you are doing it.