Should there be a problem making a Time Machine Backup with a sparse disk image containing a bootable installer on my current drive and volume?

I am trying to make a virtual machine using VirtualBox. I have been following the comment David Anderson made for me here on this post (his comment I am talking about is at the bottom): Install macOS Sierra on VirtualBox?

I have gotten to his step #3 and finished it. I am now at step 4, but I haven't started step 4.

Before I finished this process I thought it might be a good idea to make a time machine backup of my drive in case I do anything wrong, also I haven't made a backup in about 150 days.

I'm just wondering if making a Time Machine backup with a sparse disk image containing a bootable installer will be a problem for the Time machine backup?

These are my computer specs in case they are needed for reference:

Macbook Pro mid-2014, Running macOS High Sierra 10.13.6 (natively)

I would absolutely encourage you to stop and make a Time Machine backup. There’s no harm in trying to manually twiddle things, but wouldn’t it be better to make your first backup in 150 days to an actual drive that’s connected?

You won’t run into issues with installers being downloaded - those are just are large files that get saved one time and then don’t change in the next hour’s backup.

At best, Time Machine will preserve the "sparseness" of the "sparse disk image containing a bootable installer" (saving space). Otherwise, Time Machine will "fill out" the backup to the maximum size of the sparse file. Which Time Machine does may depend on whether the backup is local or remote (and possibly other factors). In either case, Time Machine should do its job and backup the file.

However, there are some restrictions on what Time Machine excludes which may affect your Time Machine backup (so YMMV):

https://www.baligu.com/pondini/TM/11.html

For example, if you have excluded your home folder/desktop where the file is located, it will be excluded.