Can I monitor my AGI as I go through the process but prior to completion? If we file MFJ we must keep our AGI under a certain amount for healthcare reasons or file MFS

No. There is only a refund monitor. 

You can look at your Tax Summary though: 

1. Log in to your tax return at TurboTax.com. 
2. Click on Tax Tools on the left side of the screen (you may need to click on Continue in the center first). 
3. Click on Tools. 
4. In the box that pops up in the center, click on View Tax Summary.