Should a System Administrator handle office furniture moves,setup and procurement? [closed]

Yes. In small and medium-sized businesses, it is not uncommon for IT departments to be deeply involved in (or even entirely responsible for) furniture.

Why? Because your predecessors demanded it. At some point in the past, an office manager or secretary was tasked with organizing a furniture build-out. When it came time for the new employees to move in, the IT administrator was asked on short notice to install a few dozen computers and phones. But, because he was not consulted when the furniture was installed, there were no network drops, the electrical outlets were in all the wrong places, the desks had "modesty panels" shoved against walls so that nothing could be plugged in without moving 300 pounds of dead weight away from the wall and back. A circuit breaker tripped every time someone tried to use the copier. Extension cords were run "temporarily" across the floor to the pod in the middle of the room, until your boss tripped over it and broke his arm. You get the idea: you are going to have to live with the consequences of furniture planning, so it is essential to get involved early and be an advocate for the "obvious" stuff like power and network connectivity.

Take your responsibility for furniture and run with it. Your job, after all, is to be a steward of function. If there are meaningless aesthetic decisions to be made, delegate them to people who care about such things. If you are responsible for the actual installation of the furniture, make sure you have a budget for someone to get it done. If new network cabling is needed, hire a contractor to install a new patch panel and run cables to the new wall jacks. If you have one 15-amp circuit for 10 new employees, hire an electrician.

But, don't insist that someone else should be in charge. You'll probably regret it.