Yes it will, because there is no need to swap the bits.
Edit:
Endianness has effect on the order in which the bytes are written for values of 2 bytes or more. Little endian means the least significant byte comes first, big-endian the other way around.
If you receive a big-eindian stream of bytes written by a little endian system, there is no debate what the most significant bit is within the bytes. If the bit order was affected you could not read each others byte streams reliably (even if it was just plain 8 bit ascii).
This can not be autmatically determined for 2-byte or bigger values, as the file system (or network layer) does not know if you send data a byte at a time, or if you are sending ints that are (e.g.) 4 bytes long.
If you have a direct 1-bit serial connection with another system, you will have to agree on little or big endian bit ordering at the transport layer.