Let $ A$ be a quiver algebra over a field $ K$ (maybe we need algebraically closed?). Then the following is two statements are well known:

1. In case $ A$ is representation-infinite, every Auslander-Reiten component contains indecomposable modules of arbitrary large dimension.

2.In case there is an indecomposable modules of dimension larger than $ max(2 dimension(A),30)$ , $ A$ is representation-infinite.

Question: Can those two statements be generalised from the category $ mod-A$ to certain subcategories of $ mod-A$ that have Auslander-Reiten sequences, maybe when replaying the bound $ max(2 dimension(A),30)$ by some other finite bound? Im especially interested in the full subcategory of Gorenstein projective $ A$ -modules in case $ A$ is Gorenstein or some other functiorially finite resolving subcategories.