You could do that.. or you could work out what key the song is in and then play through all the modes till you find the one that feels right. If it's in G Major, then all the notes in the G Major scale are going to sound right, though there are always going to be dominant notes that sound better.

The reason the Amin chord sounds good in the G Major key is that it shares the notes of the G Major scale. So while a A min chord is being played, the notes of a G Major scale will work equally as well as the notes of the C Major scale, since the notes in the Amin chord also share the notes in the C Major scale. The dominant notes while playing the Amin chord are of course A C and E, the notes that are used to construct the Amin chord. That E is going to have a different tonal centre when the G Major chord is playing though. The interval between A and E is different to the interval between G and E.. so you will get a different colour/flavour/feeling when playing the same note on top of different chords.

The pentatonic minor scale is made up of the 5 dominant notes within that minor scale. I think it's the 1st, minor-3rd, 4th, 5th, and minor-7th. The rest of the notes (2nd and 6th) are left out of the pentatonic minor scale but they can just as easily be added and still sound good. Learning where the relative major scale starts and ends in a variety of places is a good place to begin in my opinion. When I first got stuck into the major scales I only really learn the two main positions, ie. starting on the 6th string (low-E) and 5th string, using almost the same shape for each:


The first one is the standard 6th string Major scale pattern:
|--7--|--1--|-----|-----|
|-----|--5--|-----|--6--|
|--2--|-----|--3--|--4--|
|--6--|-----|--7--|--1--|
|--3--|--4--|-----|--5--|
|-----|--1--|-----|--2--|


The next is the standard 5th string Major scale pattern:
|-----|--5--|-----|--6--|-----|--7--|--1--|
|-----|--2--|-----|--3--|--4--|
|--6--|-----|--7--|--1--|
|--3--|--4--|-----|--5--|
|-----|--1--|-----|--2--|
|-----|-----|-----|-----|
[notice that you run out of room.. you can slide up on the
G string to make it sound better rather than ending up playing
4 notes on the one string.]


This one still starts on the 6th string but it's like a mirror
image of the first pattern:
|-----|--6--|-----|--7--|--1--|
|-----|--3--|--4--|-----|--5--|
|--7--|--1--|-----|--2--|-----|
|-----|--5--|-----|--6--|-----|
|-----|--2--|-----|--3--|--4--|
|-----|-----|-----|-----|--1--|


Here's another variant, this time starting on the 5th string:
|-----|-----|-----|-----|-----|
|-----|--7--|--1--|-----|-----|
|-----|--5--|-----|--6--|-----|
|-----|--2--|-----|--3--|--4--|
|-----|-----|-----|-----|--1--|
|-----|-----|-----|-----|-----|


Believe me.. they may be the same notes but your mind will see it differently and you will behave differently as you play them. Having just these 4 moveable shapes/patterns to work with will open up a whole new world of opportunities to play with. Remember also that an E over one chord will sound different when played over another chord.