5v AC Adapter with multiple outputs

They are commonly known as "console cables" or Rollover cables. They are NOT Ethernet! They are often flat CAT3, or just 8 conductor ribbon cable. All console cables are null modem cables, it is just the pin out that is sometimes different.

This will work, but what's the advantage to you over cleaning up existing cables and keeping the switches in the local racks (do you have lots of cross connects between the racks that could be eliminated?).
Remember that patch panels don't magically make your wiring neater: Discipline, maintenance, and lots of velcro ties do that.

Generally, separating your racks can be a good thing, particularly since patch panels usually come with nice solid trunks from panel to panel (less junk under the floor or in your cable trays).
The big downside is that if you lose link on a switch your now have a lot more to troubleshoot (is it the cable from the server to the local patch panel, the panel-to-panel trunk, the cable from the patch panel to the switch, the switch itself, the server itself, etc.).
The smaller downside is having to open two racks to connect a server to a switch. This can be argued as an increase in security however (someone with keys to the switch rack needs to be around to connect new equipment.

Small bit of advice no matter what you decide to do: Document the hell out of your cabling - ESPECIALLY if using patch panels. You will thank yourself later when you need to figure out what path a server takes to get to a switch port. (There are a few questions here on cable labeling schemes - https://serverfault.com/questions/64259/what-is-the-most-effective-solution-you-used-to-label-cables is one of them)