There are two actors in defending against WannaCry.
On the one hand, there is Microsoft, responsible for fixing the worm-like spreadability mode, leveraging as you said the MS17-010 vulnerability and using the exploits EternalBlue and DouplePulsar released by the Shadow Brokers.
On the other hand, there are the antivirus vendors, that need to update their signatures to actually protect the system.
So, if you install the patches (guess you are referring to Microsoft's patches), you're protecting your network from the point of view that you are not allowing the malware to spread through the MS17-010. However, you still need an updated antivirus to protect the files in your system.
For completeness' sake, as knbk pointed out in his answer, WannaCry may infect other machines in the network without exploiting MS17-010. That would be possible if those machines have shared volumes with the infected host, but if that's not the case, WannaCry uses the exploit to move horizontally throughout the network, therefore reaching more computers. Precisely, this worm-like behavior is what made it stands above the rest of ransomware out there, because usually ransomware rely on tricking the user to get infected.