Should I invite my idle team mates to participate in our project discussion with our professor?
In an ideal world you would have worked this out with the professor long ago. But you can't turn back the clock. 

Depending on the project and the professor's expectations, declaring yourself the sole worker can be a terrible solution. Especially if the prof was expecting you to learn about teamwork. 

I suspect your best course is just to turn it in and not discuss process more than necessary. 

Whether you discuss it with them or not is another matter. I don't know what your goals would be in that. I don't actually see much positive that could come out of it. Since they are nominally on the project they need to see the result, I think, before it is submitted. 

But, your professor is partly to blame here for not monitoring your work more closely. 

Unfortunately, out in the real world, this is often the outcome on joint projects. Sometimes for good reasons, though not always. 



With the comments, I'm not sure, now, about your real concern. If you are worried that you will be downgraded because you didn't actually work as a team, then it is what it is and there is a record of it in the logs. But if the prof is happy that somehow the work got done, even if all by one person, then you don't seem to have any risk here. 

The prof has established a process for evaluating your work. If it calls for a meeting of the team with evaluators then you will just have to do that, but be honest. Dishonesty often leads to the worst outcome. But if it doesn't require such a meeting, don't offer one. If you are happy with the work your grade will properly reflect your work. 

But, it might also be a mistake to claim, in a meeting, that all the work is yours. It would be better if the team mates first give an honest appraisal of their own contributions. If it is honest, then it is clear that the work is primarily or wholly yours. But that is better coming from them if they are willing to be honest. If you meet with them, I'd suggest you let them know that you will be honest with the evaluators and not try to cover for them. 

Your team mates may have to offer explanations about why they didn't participate, but that is "on" them, not you. 

If you were my student, I'd be unhappy with you, but I'd also realize that this is a learning situation. My unhappiness would be, primarily, that you didn't let me know earlier so that I could help you formulate a team more effectively. 

The tone of your question, however, doesn't raise another issue that sometimes occurs. Sometimes a "team" member will just cut out the rest of the team and do the work him/herself, ignoring the others. I don't see that here, of course, but it is something that professors need to watch for and halt when it occurs. Team work is an important skill in computing, but it isn't the most natural thing in and educational environment where students are often forbidden to work together before they reach this stage. But it needs to be taught, and that is the responsibility of the professor. 

The actual project code here isn't the most important thing. Learning is. Learning about systems, certainly, but also learning about process. 

Again, in the real world, a manager would probably be happy that the work was done, no matter how. But in the real world the product itself has a much higher value than the process. But a professor should be much more concerned with the learning, compared to the product.