Not with TEdit, but if you use TMemo and set its heigth to Edit's default, you will achieve exactly this.
Actually, that's just what TMemo is -- nothing else but multiline edit.
So the answer to your question is yes, as TMemo is "these kinds of controls" -- it's a TCustomEdit's descendent.
For grid... you can set any control to be cell editor. The default is some kind of TEdit, but you can use TMemo. To understand how to use a control as cell editor, open example project "gridcelleditor", which you will find in <your lazarus folder>\examples\gridexamples\gridcelleditor. This is very simple application which shows how to use ComboBox as cell editor for third column of string grid.