Do RNA modification proteins bind to specific repeats on the RNA polymerase II CTD?
In attempting to answer questions about protein structure, the first port of call (which one might expect the questioner to have also visited) is the Protein Data Bank — the global repository of such structures. There one can search for RNA Polymerase II CTD, look for complexes with other proteins, find recent publications in which they are reported, and consult them to find the state of knowledge of a topic.
Knowing nothing of the protein in question, I adopted this approach, and after looking at a few proteins and a few papers the following points seemed to emerge.

The CTD has a series of 7-amino acid (heptad) repeats — in mammals 21 of these are consensus(YSPTSPS), and 31 non-consensus (K7, rather than S7).
Further heterogeneity is afforded by phosphorylation (especially) and also glycosylation and proline isomerization, together with modification of the lysine of the non-consensus repeats.
It is thought that different post-transcriptional modifications are responsible for differential activation of 5′-capping or 3′-processing enzyme activities.
The CTD is disordered (unresolved) in the crystal structure of RNA Polymerase II, indicating that in the protein itself it does not adopt a fixed structure.
There are no structures of the CTD complexed to proteins it activates, so the question cannot be answered definitively.
There are structures of proteins complexed to short peptides (10- to 19-mers) based on the repeating sequence. These suggest that the structure of CTD in the complexes may be a spiral bound by specific interactions in a groove. The spiral formation may involve hydrogen-bonded β-turn motifs. A deduced structure from one such study with a 10mer is shown, together with indications of specific protein–protein interactions.


(Phosphorylated 10mer based on CTD complexed to the conserved CTD-interacting domain of mRNA processing factors RPRD1 and 2 — Adapted from Ni et al., Nature Structural and Molecular Biology (2014) 21, 686–695)
Concluding Remarks
The question contains two invalid assumptions — that proteins that interact with the CTD should interact with a single repeat, and that repeat should have a compact structure. Nevertheless, the functionality of the repeats and whether there are multiple interactions are valid questions. It appears from discussion in the paper by Ni et al. that the interacting unit is a 24-mer that binds to a dimer of the interacting protein (CID), and they propose that for phosphatases (and I presume protein kinases)15 molecules interact with the CTD at once.
What the situation is with 5′-capping or 3′-processing enzymes is another matter. There will only be one mRNA emerging from the RNA polymerase, so multiple binding would appear to make no sense. How much of the CTD is needed as rope to attach the processing enzyme soap? Does the soap slide along the rope? One would hope that eventually such questions would be answerable by molecular visualization techniques (see e.g. this BioRxiv preprint).