Ditto so many in this thread. You can but why would you want to? I'm responding sitting next to my two week old daughter. Ive done 4 IMs. For me, I couldn't imagine resuming training shortly for an IM. I couldn't imagibe leaving her to go on a long bike or run right now. Something's got to give somewhere...when you put too much on your plate, everything ends up half assed. Your training will fall apart, you'll not get the most joy out of your little newborn, the relationship with your husband will be strained (esp if he thinks you're crazy to start), your toddler will feel the strain, etc.

Why not do something shorter or focus on something specific (faster swim/bike/run)?