Yes you can, but data must be turned on. You won't be charged for sending those pictures BUT the issue is if you're using any kind of smartphone, things may update in the background once you turn it on and then you'll be charged for those. So it becomes a tricky situation.
Some Androids and Windows Phones allow you to edit the APN settings to make sure data only works for MMS but it depends on the phone you have.
An alternative is to find a different method of sending the photo; ie. BBM, WhatsApp, Facebook, email, etc. They work with WiFi only.