"The correct operation for a 'C' compiler that encounters a single-line comment of // is for the compiler to ignore absolutely everything that follows on that line, up to and including the next CR/LF. It is not important whether there is a line-continuation sign at the end of the line because the compiler should ignore it--and everything else that follows //."

But K&R specifically lists line-splicing (the backslash thing) as occurring before comment removal - so a backslash on the end of a // comment should have the effect of splicing the next line into the comment.
This does, in deed, seem to be the action of the C51 v6.14, MSVC, and BCB compilers - but MSVC and BCB are good enough to warn you about it!