That depends. If you have unlimited text and picture messaging (you probably do) Koodo won't charge you for the data usage required to send a picture. BUT if your phone uses Koodo's cellular data for other functions (like Facebook updates, for example) you will start to accumulate charges. Your wifi connection is not guaranteed and your phone will take the path of least resistance to use the internet.
Only enabling data to send picture messages while being connected to wifi at the same time will certainly minimize the risk of additional charges.
You can also turn off automatic updates for your applications to further reduce the risk.
But to be able to avoid charges entirely, you'd have to turn it off and leave it off.