In theory I dont think Id have to, but the one time I closed dimension while it was processing the file finished with just a blank background.
Even when I have it rendering in the cloud dimension still uses a ton of system resources on my 2017 MBP, so Id love to just close it and check on the process when Im ready.
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the correct workflow is;
1, design the scene
2, save the Dn file
3, then rendor (local or cloud)... assuming you saved the Dn + the actual file has finished uploading to Adobe server then no you don't need to keep Dimension open and yes it does take more from your system to keep it open