You can do this in Indesign, setting alignment to top, middle or bottom using Object Styles. I'm not 100%, but I don't think it's available in Illustrator.
When working with text in Illustrator use Area type text. Here is a little trick I use: I constantly switch between point and and Area type. (Menus - Type - Convert to X type) I use it so much I have the toggle for it as a hotkey on F6. Start by creating a textbox and enter your text. Then convert to Area and resize the textbox and place it where you want it. Afterwards, you can convert to Point and scale the entire text without the text changing lines and 'overflowing' as it would if you only increased font size using Area type. Remember to scale proportionally using Point type so you don't get stretched text. If you need to add more text, jump back to Area type and your text will stay inside your box. Hope that helps.