Absolutely - I think the main point is an open dialog with your manager should help to clarify things.
Imagine for a moment the company is doing poorly, this is a big client that they have to please, because it could mean the future of the business and all of your jobs. They may not have the money for more resources and they may not be able to re-route other people from projects since they need to close those deals as well. Ultimately it may be up to you to help deliver on that project and keep things moving forward, or you’ll all be out of jobs.
Your manager probably isn’t going to tell you that. It would create fear, rumors, doubt, and all kinds of other things that are bad for the business. But they should be able to try and figure out what can be done to make sure the work is finished on time, even if it’s dangling a carrot of promotion in your future.
Ultimately businesses are complex things, but starting the dialog will help.