This is not point is outside becouse after this you do modulo.
The question propably was when the point are outside after finished addition -> so after reduction modulo.
that what have you below describe is not right, please show how to get point outside of the field after reduction modulo. I will give you 100 BTC:)
1. Is it possible to know when the point addition process has gone outside of the field?
Implement a check before you do the modulus (I assume you made your own Point class) looking something like this:
x = # x point calculation
y = # y point calculation
if x > p_order:
print("X out of range: {}".format(x))
if y > p_order:
print("Y out of range: {}".format(y))
x %= p
y %= p
This will make your point addition much slower but it's also the only way to detect whether the addition went outside the field.