Is a mixed-effects model equivalent to an animal model in which all animals were founders?

My question is if it will be equivalent an animal model with all 
individuals being considered founders to a mixed-effects model without 
considering the A relationship matrix. In the animal model, if all 
individuals were founders the A matrix will be a identity matrix, so I 
think that both models could be equivalent, but I am not sure.

The purpose of this question is to make use of some specific programs 
(developed to estimated variance components) to run some mixed-effects 
models without considering the relationships among individuals.

Thank you.