No they wouldn't do that. The PC market is way too fragmented at this point in time. That means nobody (like on OS X) simply updates every time a new version is released. So they would have to push the game out for every single market share and the biggest ones are win 7 8 and 10 right now. You might have some problems with vista or xp, but usually you get hot fixes from the community to make the games run on those old machines.
That being said, ME:A will most likely be developed on the DX12 basis, which previous windows version will not support (this should serve as an incentive to update to win 10). If they utilize dx12 properly then you probably won't be able to use some new fx technology and your game will not look as good. Also performance is probably going to suffer if they utilize Asynchronous computing when developing, among other new features.
As for the difficulty, it's not that hard. They're basing everything on dx12 and just look at what they need to cut out when porting downwards. They basically only have to one port though. It doesn't need another version for each operating system but rather which API the OS utilizes. In case for win 7 and 8, it's both directX11 released when win 7 came out. And this will as it seems right now relatively easy. I haven't looked through all the dx12 changes so I can't tell you the exact amount of extra dev time to do this but it is fairly minimal, so no worries there. They have done that for so many games already and I've really seen no studio not doing that. Windows itself is also apt to fix possible dependency issues so this is something I wouldn't worry about.
As for the end of the extended support data. The only thing that really says is that Microsoft will stop updating and pushing security updates for the OS. This is more important for corporate clients since they have contracts which entitle them to a certain support and fixes but that support will also fall off at the noted date for windows 7.