What browser are you using? Most probably, your browser does not support the symbol font out of the box and therefore defaults back to Arial. My guess is that it will work on IE, but not on other browsers. This is because Symbol isn't a default web font.
To overcome this, you must use the @font-face rule in your css and provide the font file as a baggage file in your project. For more info on @font-face, see: http://www.font-face.com/.
I am using FireFox. I work in a high-tech industry, and it's my impression from my coworkers that most of our customers use something other than IE. We were using Mif2Go for our online help in our previous release, and I am surprised that RoboHelp can't handle this the way that Mif2Go can.
Looks like I have to try the approach you are suggesting or stick with Mif2Go.