Maybe? You'd hope, but who knows. Still easy to just replace the image with plain text in the HTML, or a data URL (if allowed). Or put an iframe in there. Point is, if they control the HTML they can do pretty much anything.

Edit: Just tried it with Chase, Merrill Lynch, Citibank, Bank of America, and Wells Fargo. Only Wells Fargo had a CSP in place to prevent this. But even Walls Fargo let you just inject a data URL image.