This is exactly what we have done with our 16 week old pup. He has been with us for 3 weeks now, and is getting really good about going to the backdoor when he has to go out.I never used the crate as a potty training tool, I only used it to keep the puppies confined when I couldn't keep my eyes on them, or when I needed to leave. Other than that, they were out and about the house with the family, but under constant supervision. And, I mean, constant 100% eyes on the puppy type thing. So, if they wander around, you follow, and see what they are doing.
This way, you learn quickly what the signs are that they need to pee or poop: excessive sniffing around, or circling, or appearing agitated, and you can take them out before they have an accident. If you're watching closely enough, you should be able to prevent accidents.