Based on the U3818DW "Operating system:" driver page, no, not supported or tested.
If we open the actual driver details, it shows =
Windows 7, 32-bit
Windows 7, 64-bit
Windows 8, 32-bit
Windows 8, 64-bit
Windows 8.1, 32-bit
Windows 8.1, 64-bit
Windows 10, 32-bit
Windows 10, 64-bit
The U3818DW User's Guide only mentions Windows.
You will need to search on the Ubuntu Forums to see if any one has tried it.
I see that you have drivers for Windows but most computers don't need special drivers for Monitors. For instance, I know this monitor works with MacBooks which also have no drivers. Drivers are generally only for "Special" features of a monitor no normal operation. I guess I could buy it and if it doesn't work with my laptop use it with my regular computer.
I am using the DELL U3818DWH with Ubuntu 18.04 and an AMD 7750.via DP cable.
The screen drops out sometimes for a few seconds (using the Linux open source "radeon" driver as well when using the AMD open source amdgpu driver.
This could be an cable, hardware or driver issue on my side, not sure (no time to test it further). But I can find more reports for these drop outs in the forum here.
There is now minimal user interface available (ddccontrol) that supports to change the screen settings for brightness, contrast, PBP/PIP and input sources for the DELL U3818DW:
Currently you have to install the update manually (until the Debian package is updated and available for downstream derivates).
PS: If you cannot find a 3840 x 1600 resolution the Ubuntu display settings you have to modify a configuration file using the `cvt` tool (watch out not to getting "headless/blind" after a reboot with untested settings ;-)