I don't think that's correct. In terms majority of ancestry in Finns is from CWC like population direct or indirect, also bulk of Finnish mtDNA is CWC in origin. While CWC had EHG ancestry Finns certainly don't descendant from some isolated EHG population. I think direct EHG ancestry from local foragers is minimal in terms of overall ancestry.
https://www.nature.com/articles/s41598-017-05673-7
Bayesian phylogenetic analyses suggest that most of these attributed Finnish lineages date back to around 3,000–5,000 years, coinciding with the arrival of Corded Ware culture and agriculture into Finland.