Agreed, like Ecky said win7 won't be supported that long. Jan 14th 2020 is the end of support date. Mainstream support has already ended meaning if an application doesn't run well on win7 due to a problem with the operating system being old or out of date don't expect any functionality fixes. Beyond end of life for a product MS continues to provide security only patches to help prevent people becoming victims of exploits in the older OS. That's what will continue to 2020.
The question of 'can' you, that's a different matter. Just like you 'can' run a pc without a firewall or antivirus. It's not recommended at all, but there's a difference between 'should' and 'could'. You potentially 'could' but 'shouldn't'. Skylake will run on windows7 yes but will everything else you use? If an os no longer supports a game, editing program or whatever other software you use then eventually the pc will become more and more useless.
It goes both ways, software can both be too new or too old for a given pc. I've got some games that used to run flawlessly on win98/xp that don't play well with win7 and crash. They rely on outdated software that was current at the time. It's one of the reasons why businesses often end up running older pc's, newer pc's may break the software they use every day. It may be too expensive or there might not even be a newer version of the programs they use and rely on. Eventually though they will need to find software to replace it with to upgrade it because hardware eventually breaks and it can be extremely expensive or impossible to find old hardware.
You can put that pc together and run win7 on it, just don't expect it to last 4, 5, 6+ years. Technically skylake is already outdated by kaby, kaby lake has been out awhile and soon enough there will be yet another new generation of motherboards and cpu's as well as future programs built around the newer win10 (already almost 2yrs old).