Does $T$ having the order property simply mean that there is a formula $\phi(x_1,\ldots,x_n,y_1,\ldots,y_n)$ and model $M$ of $T$ such that $\phi$ defines an infinite linear order in $M$ on some set of $n$-tuples of elements of $M$?
Is this the same as interpreting an infinite linear order in some model?