Not necessarily. If you'd drawn the match 0-0 instead, your goal average would have been unchanged and therefore slightly inferior to the GA improved by the 2-3 defeat.
Not sure what you're saying there but take this example: You've conceded twice as many as you've scored but then go and lose 2-3.The revised ratio is slightly improved whereas if you had lost 2-4, it would be unchanged.
I didn't know it was that close; always assumed the closest was in 1988-89 when Arsenal's unlikely 2-0 victory at Anfield in the last match won it, whereas a 1-0 victory would have resulted in their opponents becoming champions instead.
That was only true for teams at the top. For relegation issues, i.e. in cases of negative identical goal difference, the higher scorers had the advantage. The fact that you could improve your goal average by losing (and vice versa) showed the system's illogicality.