It should be fine. Apple themselves offer to sell you a 27" display along with the laptop so it clearly is capable of driving that many pixels.
I myself use a 15" 2012 MBP Retina with one of those mini DisplayPort to Dual-Link DVI adapters (hooked up to a Hazro 27" monitor, so cheap no-frills much like you're considering) and its been pretty good. This is in addition to also driving a cinema display of the same size, so I have two external monitors.
I read a lot of reviews around the Internet before buying it, and there's a few horror stories (most of them say make sure you get one with firmware 1.03, but there's no way to tell what firmware you have, till you plug it in! - fortunately mine was 1.03 from the off).
The only issue I have with mine is occasionally (maybe once or twice a day) the Hazro monitor goes blank for a second, then comes back on. I have no idea whats causing this, the MBP doesn't even notice (doesn't try to rearrange windows or anything) and its infrequent enough that I just live with it. It may be a slight incompatibility between some of the equipment.
I do suffer from some occasional oddities if I unplug the external monitors while the MBP is asleep, then wake it up (the internal screen won't come on, I think its the graphics card drivers crashing at the unexpected situation) but I don't believe thats related to the Dual-Link DVI.
I've used Teleport, a really neat pref-pane that functions as a software-only KVM switch. Moving the mouse off of one screen onto the next accomplishes the switch. I used to use it with a Macbook and an iMac next to each other on my desk, controlling either one with a single keyboard and mouse.
Best Answer
After weeks of trial and error, I have finally achieved 2560x1600 resolution on my Apple 30-inch Cinema Display connected to my MacBook Pro,15-inch, 2016 laptop.
The trick is to go from USB-C to Mini Display Port (MDP), then to dual-link DVI. Unfortunately, this does take two adapters, but at least the full monitor's resolution is supported.
I used the following adapters:
Also to note, the DVI adapter needs to be powered by the attached USB connector, and the monitor break out cable USB also needs to be attached to the MacBook.
A bit of a cabling challenge, but everything is now working 100%. Andreas came up with a substantially similar solution, but with different brands and gets the answer bonus!