No the king can not be checked during the “middle position”
FIDE laws of chess:
3.8 a. There are two different ways of moving the king, by:
i. moving to any adjoining square not attacked by one or more of the opponent's pieces.
or
ii. 'castling'. This is a move of the king and either rook of the same colour on the same rank, counting as a single move of the king and executed as follows: the king is transferred from its original square two squares towards the rook, then that rook is transferred to the square the king has just crossed.
(1) The right to castle has been lost:
a. if the king has already moved, or
b. with a rook that has already moved
(2) Castling is prevented temporarily
a. if the square on which the king stands, or the square which it must cross, or the square which it is to occupy, is attacked by one or more of the opponent's pieces.
b. if there is any piece between the king and the rook with which castling is to be effected.
