I haven't ridden the entire TransAmerica route but I have used both warmshowers.org and couchsurfing.org hosts extensively in my bike touring, some of which was on the TransAmerica route.
Is it possible? In a limited way, yes. You can only be hosted where there are hosts. This is why I use couchsurfing more than warmshowers because there are many (times) more couchsurfing hosts than warmshowers hosts. The more remote the place, the less likelihood you'll find a host. As I mentioned on a previous thread, the more you are relying on other people to host you, the better your planning has to be. I often get last minute requests from people to stay at my house. I usually refuse as I am busy, like to plan to have visitors, and want some time to interact with potential guests before offering hospitality.
Also, I don't know outgoing you are but it helps greatly if you enjoy spending time talking with friendly people you have just met. Can you converse with people you've never met for, at least, an hour? If not, then you might not find spending night after night with strangers all that much fun. Nothing like spending 6 hours riding a bike to someone's house only to discover you have nothing in common and are uncomfortable at the house.