Yes, it is a linear constraint. $x+ry\geq 12$ is linear for any constant coefficient $r$. The fact that you know additional information about $r$ (namely, that it happens to lie in the set $[2,3]$) does not change the linearity of the constraint.
For example, $px+y\geq 2$ is also linear for a coefficient $p$, even when you know that in particular $p=4$. The key thing is that the coefficient is a constant and not a variable.
You mentioned that the constraint is "not defined everywhere where x and y are". Perhaps a misconception. The constraint is defined using the constant $r$, (which we know lies in $[2,3]$), but that doesn't mean the constraint only holds for $x,y\in[2,3]$ or anything like that. Instead, the constraint is defined for all real $x$ and $y$.