No, lsp, not necessarily... a scar is something more, it implies being very hurt...
Segnare profondamente significa soprattutto lasciare il segno, lasciare un segno indelebile.
So now I have several expressions to choose from
That fact has left a deep mark on me
That fact has affected me deeply
That fact has affected me profoundly
That fact left a profound mark on me
That fact has marked me for life