First lets be straight you aren't deleting it, but as it says on the tin 'Move to Chest.' So it is literally moved to the avast chest and that is the only place it exists.
Files in the chest are encrypted and can't be accessed from outside the chest. You can access the physical chest folder using windows explorer, but you won't find the file that was moved there as the file name is also changed, so to applications they see only the name generated by avast, but they still cant do anything with it.
How do you know if a file is unimportant ?
Answer you probably don't, so what happens having deleted it, you are up the creek without a paddle and no more options, deletion is in my opinion crazy. It must be fully investigated and confirmed there would be no problem, which you can't do if you have already deleted it.