No, "Fit Node to Label" will not help with that. The available positions of labels are determined by the label's "Placement" property (select the label and see the properties view in yEd's lower right corner or type F6 to open the properties dialog). When editing the "Placement" property a small dialog is shown with options "Model" and "Position". Some models (like e.g. "Internal") will allow for specific positions only while others (like e.g. "Smart Free") will allow for arbitrary positions (i.e. the "Position" drop-down list has an entry "Anywhere"). If you want to place the label manually using the mouse, I recommend "Placement" model "Smart Free".
Since you are mentioning values "Center", "Left", and "Right", you are probably trying to adjust the label's "Alignment" property instead of its "Placement" property. "Alignment" governs the text alignment inside the label bounds (and thus has a visible effect only for multiple lines of text in one label) whereas "Placement" determines the label placement in relation to the labeled element (i.e. node or edge).