Yes. The easiest way would probably be using a form of an array.
Construct an array, remove the line, then write again, ignoring lines that are blank.
%f = new FileObject()
%f.openfileforread(blah);
%i = 0;
While(!iseof(%f))
{
%f.line[%i] = %f.readline();
%i++
}
%f.close();
%f.line[4] = "REDACTED";
%f.openforwrite(blah);
For(%j = 0; %j < %i; %j++)
{
If(%f.line[%j] !$= "REDACTED")
%f.writeline(%f.line[%j]);
}
%f.close(); %f.delete();
forgeted something up, I'm sure. I blame the phone in advance.