It is only possible, if the file is opened for reading by a third-party, but not for writing.
If the third-party opened the file for writing, your attempt to open the same file even just for reading will result in System.IO.IOException. In fact, it's all about FileStream and not specific to EpPlus and ExcelPackage. Example in terms of .NET:
var fileStream1 = new FileStream(@"File.ext", FileMode.Open, FileAccess.Read);
var fileStream2 = new FileStream(@"File.ext", FileMode.Open, FileAccess.Read);
will work just fine. But the second line of the following fragment:
var fileStream1 = new FileStream(@"File.ext", FileMode.Open, FileAccess.Write);
var fileStream2 = new FileStream(@"File.ext", FileMode.Open, FileAccess.Read);
will result in a System.IO.IOException.