You can do it...but it's not necessarily a good idea. As CPallini says, if you are looking for a line end in a binary file - which don't have lines, just eight bit binary values - then you will have problems. And even if the file contains text, the actual data stored in the file to indicate the "end of a line" can differ from system to system: "\n", "\r", and "\n\r" are pretty common. So checking yourself can get complicated.
Instead, why not treat the data as the format it was written? Assuming it's text (or newlines are the least of your problems) just use:
string[] lines = File.ReadAllLines(path);
Or just use ReadLine with your StreamReader:
https://msdn.microsoft.com/en-us/library/aa287535(v=vs.71).aspx[
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And let the system sort it out.