I may have misunderstood what you're trying to do (there's something to be said for using familiar artists in your examples, though I'm sure Amorphis are lovely folks), but I set up a small test and got this:
Thumbnail Browser is showing
V: Artist Group, grouped by
Album Artist.
V: Artist Group is just this virtual tag:
$IsNull(<Original Artist>," ",<Original Artist>)
Artist for all albums is "Mike Patton",
Original Artist is the side project name.
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.