I would love to play in a worship band that did more improvisation, as a musician I live for extended jams and free playing. At the same time I have to wonder if including extended improvs is contrary to the band's primary role -- to lead the congregation in worshipping God through song. As a congregant, I personally would be distracted from my worship if the band started trading 4s with the drummer, or the guitar solo went through the changes more than once or twice (depending on the tempo). Instead of focusing on God, I would be keyed in on what the band was doing. I have to confess, as a musician it's already hard enough not to focus on the band!
If improvisation was being incorporated into a regular Sunday service, it would have to be subtle and restrained. If it was a special worship service (perhaps in an evening) that was more purely focused on music, singing and praise, then by all means -- go crazy!
Regarding your other question, the best way to develop improvisational skills as a band is to jam together. It helps to work out a rough arrangement beforehand -- play through the verse and chorus, then the guitar 1 solos through the changes 2 times, then piano 2 times, and so on. There are different philosophies about improv, but to me it's all about listening to what other musicians are doing and responding to what you hear. Books and other instructional materials can help, but the only way to improve as an improviser is to listen and play.