This is the most ridiculous thing I read in months. If you want to run a server you need proper hardware. A Mac is a consumer-level machine not meant to run in the data center(or even a lab for that matter). It has no dual psu, no raid controller and no replaceable parts!! What the hell is your IT department smoking?
There is a difference between challenging the status quo and asininely defying it. In IT, there are best practices and they are there for a reason. Your approach is kind of like UPS saying "We don't like these ugly brown trucks even though they are engineered for this purpose, but we do really like these sleek Teslas, so we are going to deliver packages in them instead"
Btw, there is no such thing as a 'Mac Admin'.
Actually Linux does have a GUI if you want one. It usually gets in the way though, and besides unless you are going through some kind of IP-KVM/iLO/DRAC/whatever you going to have to use ssh instead anyway.
Btw, Linux is extremely easy to update. 'yum -y upgrade' and that's it.
Having said all that, I have no idea how big your company is. If it's something like 10 people, you might be OK. Keep in mind though that your solution won't scale at all.
Here is my most important advice to you. If(when) you look for another job, please do not under any circumstance put this project as a line item on your resume. It's guaranteed to cost you the interview.