As far as I know changing the OFS (Output Field Separator) to RS (Input Record Separator, a newline by default) and rebuilding will only alter the way awk print the records.
It will not make any difference in the original record which awk read and stored internally in its memory.
This is the reason why you get expected output while printing, but not while computing the sum.
further to Yoda, I think $0 would still contain as the original input record and performing maths would result on the integer part ( int($0) would return $1 ) in this case. (others please correct me here if this is not the case)
You have to play with RS
awk 'BEGIN {RS="[ \n]"} {s+=$0} END {print s}' file
AFAIK, I guess multi-character RS is supported only by gnu awk ( though not very much sure).