Measuring semantic similarity across languages is central to many NLP, computational social science, and digital humanities workflows, yet most high-performing similarity models are monolingual and operate in language-specific embedding spaces. A common workaround is pivot translation: machine-translate all texts into a hub language (typically English) and then compute similarity using strong English encoders. This paper tests a key assumption behind that practice—whether corpus-level textual similarity is invariant under machine translation—using the Party Manifesto Corpus (2,878 documents in 28 eTranslation-supported languages). We segment manifestos into approximately single-topic pseudo-paragraphs via sentence splitting and change-point detection, align source and translated sentences with a monotone dynamic-programming procedure, and compute pseudo-paragraph embeddings using (i) language-specific models on originals, (ii) English models on translations, and (iii) multilingual models as a benchmark. Invariance is quantified by correlating paragraph–paragraph cosine similarity matrices (representational similarity analysis) and by nonparametric tests comparing translation-induced shifts to within-language model variability. We find that translation typically perturbs similarity structure: correlations between original-language and translation-based similarity matrices are often lower than correlations among original-language models, with substantial heterogeneity across languages. However, selecting the best-performing English encoder per language markedly reduces this gap, and multilingual models are generally more stable but not universally superior. Importantly, downstream impacts on ideological classification, clustering, and dimensionality reduction are smaller than representational distortions, suggesting that translation noise often preserves task-relevant structure. The results provide language-specific guidance on when translation-plus-English embeddings are sufficient and when multilingual representations are preferable.