The converter would bring over data from your old application. It does not seem you mentioned which forum software you converted from, if it is one which we supply 301 redirects, these would indeed work.
I am a little confused about what you mean with the iframe. Iframe would still expose your forum's URLs so these are the URLs which search engines would index and thus, if you use a converter with an applicable 301 redirect tool of ours, these would be updated.
Essentially, we would need to know what you converted from and a URL which is broken that you expect to be redirected to test if it is working.