There has been some really good answers given here.
Let's take a bit of a twist on this discussion - here is another question for you:
If there was no way other than you using sign language, and there was no hearing person who knew sign, how would you communicate and successfully get your point across? Do you see that as possible or not?
I can add to this from the other side, as well as a bit from my perspective being HOH now. Becoming HOH later though means it's just incoming communication that's tough for me. For communicating to someone I have my voice.
Before I started learning sign language (in fact quite a while ago) I worked as a cashier in a grocery store. I had a regular customer who was Deaf and he'd always come to my lane if I was in. I didn't really know any ASL then beyond basics like thank you, hi, bye, money, and maybe a few other signs, stuff I learned in grade school or picked up on from this customer or other Deaf I interacted with back then.
Most of the time transactions like that can happen without really having to talk much, but sometimes things come up, a card is rejected, or someone gave the wrong amount of money, or whatever. When this happened with that customer, he'd use signs that (I assume) he knew were easy to pick up the meaning of even without knowing ASL, along with pointing. I think he was pretty good at speech reading too, but I'd add to most things I said by pointing so he had extra context.
Thinking about it now that I'm HOH, I was probably his choice because my interactions were predictable, I already knew he was Deaf, and I was easy to interact with. Personally, now, when I go to a new store, restaurant, whatever, it's a lot tougher than when I go somewhere familiar where I know what they're going to ask me. Noisy places are the toughest, I can't understand or sometimes even distinguish speech if there's a ton of background noise and someone has a softer or higher pitched voice.
I feel sorry for the poor girl behind the Qudoba (ameri-mex restaurant typically playing loud music where you order custom fillings for your burrito, quesadilla, or whatever) counter the first time I went there... had no idea it was going to be such an involved ordering process and she had such a soft voice. I think she picked up on the fact I couldn't hear her (not sure how she couldn't have) because she started pointing more and looking at me more when talking.
I think the communication effort has to be on both sides. The toughest is when you encounter someone who just can't figure out a different approach at all or for whatever reason doesn't understand that you just can't hear them. I've had that experience already too, blank stares where you know they're thinking "why can't you just answer my question, idiot" or "oh great another stupid white guy who can't understand my accent" that one almost makes me feel bad...