Is the critical path important if only one person is working in a software project?

Yes, it's difficult to handle all things at a time like coding, designing forms and as well as documentation... always prefer to work in team..that will better and you will complete your project sooner.

Critical path is usually used to define the tasks that need to be completed in order to complete a project. Depending on how good the software developer is, it could take them a short time to do each of the tasks, or a long time, or worse still take further time to find and correct any problems, so critical path is very important on any project, irrespective of how many people are assigned to the task.