If a website is localized/internationalized with a Simplified Chinese translation...
Short answer: No, not reliably+high quality. I wouldn't recommend automated tools unless the market isn't that important to you and you can risk certain publicly embarrassing flubs. You may find some localization firms are happier to start with a quality simplified Chinese translation and adapt it to traditional, but you may also find that many companies prefer to start with the English source.
Longer answer: There are some cases where only the glyphs are different, and they have different unicode code points. But there are also some idiomatic and vocabulary differences between the PRC and Taiwan/Hong Kong, and your quality will suffer if these aren't handled. Technical terms may be more problematic or less, depending on the era in which the terms became commonly used. Some of these issues may be caught by automated tools, but not all of them. Certainly, if you go the route of automatically converting things, make sure you get buyoff from QA teams based in each of your target markets.
Additionally, there are sociopolitical concerns as well. For example, you can use terms like "Republic of China" in Taiwan, but this will royally piss off the Chinese government if it appears in your simplified Chinese version (and sometimes your English version); if you have an actual subsidiary or partner in China, the staff may be arrested solely on the basis of subversive terminology. (This is not unique to China; Pakistan/India and Turkey have similar issues). You can get into similar trouble by referring to "Taiwan" as a "country."
