(It's possible you are merely neglecting to close the img-tag with a "/".)
I've only attempted this with an image saved within Clarizen and not an external link. The code/HTML to add within the email body:
<img src="{GetImage('customicon','background2')+'?w=640'}"} />
CustomIcon is standard field located on the Organization. You upload specific images via Edit of the Picklist here:
background2 happens to the name of a saved image in this example; width is option, but I would recommend.
Also, I've found the email feature's HTML interpreter to be extremely literal with spaces and line breaks. I format my HTML with no spaces (except for displayed text) and no line breaks---this results in terribly long strings of endless text, but looks best then receiving an email.