If I understand your question correctly, you want to know if gene copy number can have an indirect effect on transcription, i.e. an effect that does not arise from the dosage effects of the copied sequence or the direct disruption of proximal genes?
I think the answer is yes, insomuch that CNVs can change chromatin architecture.
In many eukaryotes, the genome is spatially organized into topologically associated domains (TADs). Though their necessity in all contexts is contested, there is mounting evidence that suggests TADs delineate meaningful associations between distal regulatory elements like enhancers and promoters.1 Duplications can be pathogenic if they occur within a TAD or across a TAD boundary.2 Deletions at a single CNV locus have been implicated in causing genome-wide transcriptional changes at loci important for human brain development via ablation of TAD boundaries.3
Note that chromatin conformation capture experiments (i.e. Hi-C) are often confounded by CNVs due to the effect of copy number on library prevalence and, consequently, contact frequency calculations, making the inference of CNV effect on genome organization inherently problematic. However, new computational tools have been implemented to account for such biases.4,5
- Beagan JA, Phillips-Cremins JE. On the existence and functionality of topologically associating domains. Nat Genet. 2020 Jan;52(1):8-16.
- Franke M, Ibrahim DM, Andrey G, Schwarzer W, Heinrich V, Schöpflin R, Kraft K, Kempfer R, Jerković I, Chan WL, Spielmann M, Timmermann B, Wittler L, Kurth I, Cambiaso P, Zuffardi O, Houge G, Lambie L, Brancati F, Pombo A, Vingron M, Spitz F, Mundlos S. Formation of new chromatin domains determines pathogenicity of genomic duplications. Nature. 2016 Oct 13;538(7624):265-269.
- Zhang X, Zhang Y, Zhu X, Purmann C, Haney MS, Ward T, Khechaduri A, Yao J, Weissman SM, Urban AE. Local and global chromatin interactions are altered by large genomic deletions associated with human brain development. Nat Commun. 2018 Dec 17;9(1):5356.
- Servant N, Varoquaux N, Heard E, Barillot E, Vert JP. Effective normalization for copy number variation in Hi-C data. BMC Bioinformatics. 2018 Sep 6;19(1):313.
- Wang X, Xu J, Zhang B, Hou Y, Song F, Lyu H, Yue F. Genome-wide detection of enhancer-hijacking events from chromatin interaction data in rearranged genomes. Nat Methods. 2021 Jun;18(6):661-668.