If a pregnancy test is not made with first morning urine, does it make a difference in the results being positive or negative?

It will be different as far as the negative goes. Pregnancy tests taken after first morning urine have a tendency to give a false negative, where if you took the same test first thing in the morning you may get a positive.

Typically a positive is a positive no matter what time of day. First morning urine is the most accurate.

I would use the first morning urine if you think you are very early in pregnancy. I got a positive pregnancy test (well more like 5) the night before my period was due and I had found out I was only three weeks pregnant when I took those tests. Some people will get an accurate reading even if it's not first morning urine. If you think you're pretty far in pregnancy then it won't matter. Your hcg levels will be up high enough for you to get a positive at any time of day. But if you're a few days late, best bet is to use that first morning urine.

It is always advised to use first morning urine, because after sleeping all night, your urine will be more concentrated with HcG if you are pregnant.