Will expand the comment a bit as an answer so we can maybe get some discussion on it for the question:
No, you probably shouldn't worry about using ems just to satisfy IE6. There is basically no reason to support this browser anymore unless you are building something targeted at a very specific user set. For example: business clients that require employees to use only IE6 on company computers.
At its latest, IE6 isn't even at half of a percent
However, you should be using ems anyway. They are more flexible and just make more sense. Chris Coyier explains it way better than I can here, so read on to find out: Why Ems? (CSS-Tricks)
EDIT:
In response to the edits/clarification that you have made, it seems like a question eithernot suited to stackoverflow (i.e. more legal than technical), or something which we don't quite have enough information to answer (likely both).
In terms of whether or not you are legally obliged to do so, that is likely something that requires even more context. I speak from a non-expert standpoint, but I would say that, at least in the US, you are (probably) not legally obliged to support a specific browser as a private business. If you are a government entity, that gets a little more complicated. If the company is based on (or perhaps even conducts a large amount of business in) another country, I can't really say much. It is probable that, in a majority of the EU countries (I can only really speak with any knowledge about Germany), the same would hold true.
If we assume the site is for a government entity or is heavily funded by the government (having said that for private entities you should not legally be obliged), the next question would be about what sort of service the company provides via the website. If it is something that you are legally obliged to allow all citizens easy access to, then you might need to worry. But, even then, I doubt there is really any issue as the service would also then be required to be accessible through a non-internet channel.
I am guessing that the question is more something like "For the website of a (large) private business, am I subject to claims of discrimination if I do not include this feature?" Or am I still missing the context? I would say that the answer is, pretty definitely, no. But I don't actually have a legally informed answer.
I hope anyone with more knowledge will edit or comment on this with more information.