Is it better to roll out a new unified communications system at once or to update gradually?

Either approach will work. Often, for both financial and operational reasons, organizations use a phased approach. The modular nature of unified communications makes it very easy to implement gradually.

However, even when using a phased implementation, you have to know what the goal is. In other words, you should still take the time to do the research and develop a comprehensive plan for what the architecture of your ultimate unified communications infrastructure will look like, and then implement the components over time to achieve that goal.

If you start purchasing and implementing components without having the ultimate UC goal in mind, you could run into problems integrating components with each other or with your existing network architecture. The consequences of pushing on blindly could range from nothing, to costly re-engineering to integrate the different phases, to being unable to make it work and having to go back to square one to implement a properly engineered solution.