You should be able to add an $IsNull() function to your virtual tag to change it to something else if it's empty.
$IsNull(<YourVirtualTag>,Other,<YourVirtualTag>)
(https://i.imgur.com/R7x2iIt.png)
Thumbnail Browser is showing V: Artist Group, grouped by Album Artist.
V: Artist Group is just this virtual tag:
$IsNull(<Original Artist>," ",<Original Artist>)
The first album has no Original Artist tag, so nothing is shown to imply that those albums are under the artist's original name.
MusicBee has an all or nothing approach to showing fields, so there's nothing that can be done to remove the blank row there.
Obviously, what works for a three album test may not work on a full library, but with the right custom tags and virtual formulas, you could probably get what you need.
-edit-
Just looked at your screenshot again and realised mine is kinda backwards.
Back to the drawing board...
-edit edit-
Tried again, but I don't think your latest mockup can be achieved.
Is there a way, not to group artists when the group by field is blank
Because the answer to this is no. When grouping, MusicBee will always resolve to group a track by something. It can be the same thing for all non-grouped tracks, but then you'll be back where you started.
Also, if this is a new tagging venture you're embarking on, I strongly suggest creating a custom tag to use for the side-project information instead of Original Artist. You might not need it now, but in a few years time when you realise you want to use that tag for something else (like for tagging your cover songs), you'll have to spend more time retrofitting all those tags first and that's not fun.
Also realised my example wasn't ideal because I had the tags the wrong way around - it would be preferable for the Artist tag to reflect the side project name and the Original artist to be the artist name.
This can be fixed by using two virtual tags:
V: Artist Group:
$IsNull(<Original Artist>,<Album Artist>,<Original Artist>)
$IsNull(<Original Artist>," ",<Album Artist>)