Resolve renders fine in 4K. The output module will let you define what resolution you want. The bigger problem will be figuring out what CODEC to use in 4K. What do you intend to do with your 4K video?
If you are going to a 4K tv, how will you input it? There are no players for burning 4K video. The best you can do with optical media is HD using BluRay.
On 4K tvs, what is simplest is to input into the tvs via the usb input. That is usually fast enough. You will need to encode to h264 (AVC) or h265 (HEVC). I don't off hand know if Resolve will encode using the h265 codec, but the h264 should work. My usual work flow is 4K ProRes out of Resolve, and then encode to h265 using Handbrake, which will do either h264 or h265.
Obviously I don't know much about resolve only having used it a couple days.
I downloaded it from this screen.

The one on the right says "Get all the features of the free version plus support for multiple GPUs, 4K output, motion blur effects, temporal and spatial noise reduction, 3D tools, remote and multi user collaboration tools."
So I assumed the free version did not support 4k rendering.
There is a 4K DCI CODEC but when I try to use it I get a 2k/4k warning and it it drops the resolution before putting it in the render cue.
I could not find other 4k options.
Highest res I could render was 3840x2160 Ultra HD
Sorry if I'm wrong, or missed something.
It is great software for free.
I will play with Resolve some more.
Although I often shoot in 4k I rarely render to 4k video. Doesn't mean I don't want to have the option.
Maybe I want to upload 4k video to Vemio because I can.
I don't have a Blue Rey player or a 4k TV.
Corel Video Studio comes with 4K codecs
I'm happy with what I have. I'm just curious and like to check out different software.
Sorry if I offended any Resolve users.