That may be possible.
My suggestion is to first get a formula checkbox field working to evaluate of that condition is true.
Now, the field [Record Owner] is a User field and also I do not believe that it exists until the record exists, which it does not do until the record is saved.
But the Record Owner will be the current user when the record is saved.
That drop down list of PIM users seems to be just a multiple choice text field.
I suggest that you make a List User field with a formula of the userids of these PIM users. You could call it [Userids of PIM Users].
for example
ToUserList("
fred.flintstone@bedrock.com",
Barney.rubble@bedrock.com")
Then have a formula checkbox field called [Current User is a PIM User].
The formula would be
if(Includes([Userids of PIM Users],ToUserList(User())),true, false)
Once you have that working and tested, then put that field on the form to ensure that the form rules see it (we can hide it later once its working)
Then have a form rule like
when
[Assigned to] is (leave blank)
and
[Current User is a PIM User] is checked
Action
Change [Assigned to] to the value
Wilma.flintstone@bedrock.com