I wouldn't have any expectations... I would go prepared to pay, so as not to get caught out.

But I do think it's best to make it clear on the invites...I think linking the restaurant is a great idea, but maybe might not be enough for some people? I would put something along the lines of not needing to bring a gift as they will be paying for their meal (nicer wording perhaps).

Also, is there an option for people who don't want to eat to join in? If there is then I would make that clear too, so people don't decline the invitation due to money troubles IYKWIM.