You "CAN" render your sequence in Software to get an easier alpha, but in your case I believe the reason you are not seeing your particle-instances when alpha is ON, is because that flag does NOT mean particle alpha.

It is a GEOMETRY mask/alpha, meaning, say you are emitting particles (instanced or not) FROM geometry to make them appear to make a shape, the "alpha on" flag will OCCLUDE the geometry from your particles, making things easier for you in post for those "around the world" effects.

So, if you are emitting your particles from geometry, you must remember that Maya wants to take your geometry into account as well when it comes to the final render.

So, if you ARE emitting your particles from geometry, make sure that in the geometry's "shape" node that you have "primary visibility" TURNED OFF.

This is DIFFERENT that just turning its' visibility off in the channel box, so remember that too

If none of that helps, I've got another idea so just lemme know