I think whether people will ask can depend on the woman's build. For instance, it's *very* obvious that I'm pregnant and haven't gained weight. So when I'm pregnant, nobody ever seems to hesitate to congratulate me without an announcement. If I tried to do something like the OP said, it would go like this:
I enter the room. Several not-shy aunts start to say, "Hi!" and then see the tummy. Immediately there are squeals of delight, "You're pregnant!" and I am converged upon. Everybody else overhears and anybody who would have hesitated to say something (especially men) are in the clear because I've responded appropriately to the initial yay-you're-pregnant aunts. So it would be fine. However, some of it depends on how obvious it is that you're pregnant, and whether you have any friendly female relatives who are likely to blurt it out. Of course, I've never gone this route, I'm more the type to tell everybody in all neighboring states about the moment that it's been confirmed by the doctor.