Yes. General case:

# line mode
...

{
   # paragraph mode
   local $/ = '';
   ...
}

# line mode
...
[download]

Your case:

sub process_csv {
   ...

   open(my $fh, '<', ...)
      or die(...);

   while (<$fh>) {
      ...
      process_file(...);
      ...
   }

   ...
}

sub process_file {
   ...

   local $/ = '';

   open(my $fh, '<', ...)
      or die(...);

   while (<$fh>) {
      ...
   }

   ...
}
[download]

Beware. If proces_file calls functions, paragraph mode will still be active. That means don't call process_csv (directly or indirectly) from process_file without fixing $/.