The answer is generally "no", simply because - as a general rule - there is no actual character in a file that conclusively marks the end of a file.
You are probably well advised to try a different approach, such as one of those suggested here: https://stackoverflow.com/questions/10984432/how-to-read-the-file-content-into-a-variable-in-one-go. Use of:
IFS="" contents=$(<file)
is particularly elegant; it causes Bash to read the contents of file into the variable contents, except for NULL-bytes, which Bash-variables can't hold (due to its internal use of C-style, NULL-byte terminated strings). IFS="" sets the internal field separator to empty so as to disable word splitting (and hence to avoid the removal of newlines).
Note: Since (for lack of reputation points) I can't comment on the answer suggesting the use of read with the -N option, I note here that that answer is - by definition - not guaranteed to work as it stands, because the filesize is unknown in advance.