Yes, it can be done. You have to use the 2014 version of Sketchup, and you have to tweak the Windows Imaging Component DLLs which are not installed by the .NET 4 installer. The .NET 4 installer only installs a couple of the 4 DLLs you need, so you have to deploy the other two and install/register them. This information is likely useful for anyone else running into "Windows Imaging Component Install Failed" or even "Cannot Update a Checked (Debug) System" types of issues. (If you got to this page after you've gotten the latter error, use the dotnetfx_cleanup_tool described here to get your .NET back to a clean state.)
I used these excellent instructions to initially install ReactOS in VirtualBox.
I then installed the "Guest Editions CD Image" under the Device menu, and installed Guest Editions. This step is optional for getting Sketchup running, but I always find it helpful to be able to drag-n-drop, cut-n-paste, between guest and host, etc. This includes enabling these features once installed, under the "Devices" menu, for example, as seen in this screenshot:
I also enabled Shared Clipboard and added a Shared Folder so I could easily move files from my host machine to the guest.
Likewise, with the optional step of installing an audio driver to eliminate the popup that appears when you first start ReactOS. Simply performing the first three steps in these instructions were sufficient for me. Finally, I had a clean vanilla install of ReactOS in VirtualBox, ready for the Sketchup install. I tried many options, but eventually, this is what worked:
Install .NET 4.0 using the link provided for Frameworks on the ReactOS site. Restart when requested.
3. Download these last two DLLs from anywhere you trust. I found the dll4free site was able to give me the DLLs without sending me into rabbitholes of malware or advertising madness. As you can see in the screenshot, I grabbed the 6.0.6001.1800 32-bit version of WMPhoto. And 6.0.6001.1700 for PhotoMetadataHandler. But if you're feeling frisky, try one of the newer versions if you want. This site also nicely explains how to install and register, which is the next step:
ReactOS\system32), then run the following command from a CMD window:
%windir%\System32\regsvr32.exe photometadatahandler.dll. Then do the same for wmphoto.dll. When you are done with each, you'll get a popup indicating success, as seen in the following screenshot:
If you need to convert a newer Sketchup file to this version, you can do this within the "Save As" prompt, and save it to 2014 version.
Hope this saves someone else the hours it took me to figure out how to do this.