Question is quite straightforward:
When Ajax.BeginForm() may ignore form submit on enter press ?
Solution:
A form MAY BE submitted without an <input type="submit"> (through) enter key press if:
There is only one html element inside the form of type <input type="text"> (with textarea doesn't work).
A form MAY NOT BE submitted via enter key press if:
There is more than one html element inside the form of type <input type="text">, and no <input type="submit">