may i know what is your basic salary per month (excluding bonus)?
And your age and gender?
And what is your role in your engineering job?

To get a reasonable paying govt. job, a full-time degree frm recognised university puts you in good stand. But since you already have about 6 years of work experience, that might compensate your long distance degree. There is no harm in applying, if they reject it, it means you should get Masters :-)

Career progression wise - again, long distance degree holders are less prioritised but if you can show the work you are capable of, then definitely nothing is impossible. And once in the job, you can do a part time masters from local university.