I was wondering if there is a way, without maybe having to read every line in the file, to quickly see if there exist lines that do not start with # (which would mean that I can process this file further.

Not really (but may the other monks correct me if I'm wrong). Since you can't know in general where a new line starts without having read all of the preceding one, you cannot know whether any line starts with a hash mark unless you read them all.

This is for the general case, of course. If the output of your program is further constrained, inferences may be possible; for instance, if you know that every line is precisely 70 characters (including the trailing newline), you could read every 70th character only. Whether that'd be much faster in practice is another question, one that only profiling could answer.

Is there any way that the program generating this output can signal to you whether there's data that needs further processing? If you can change that one's implementation, perhaps have it quit with an appropriate exit code, or drop a marker file, or something along those lines.