Do user defined data types always cause implicit conversion to occur when fields of those UDDTs are used as predicates?
I can't reproduce any warnings or performance differences in this scenario, even when joining bVarchar to varchar(10).  EG
create database tt 

alter database tt collate Latin1_General_BIN
use tt 
go
create type bVarchar from varchar(10)

create table a(id int primary key identity, b bVarchar, c varchar(10));
create table b(id int primary key identity, b bVarchar, c varchar(10));

with q as
(
  select top 1000000 row_number() over (order by (select null)) i
  from sys.messages, sys.objects 
)
insert into a (b,c) 
select concat(i%10000,'abc'), concat(i%10000,'abc')
from q;  

with q as
(
  select top 1000000 row_number() over (order by (select null)) i
  from sys.messages, sys.objects 
)
insert into b (b,c) 
select concat(i%10000,'abc'), concat(i%10000,'abc')
from q;  

go


set statistics time on
set statistics io on

select count(*)
from a
join b 
  on a.b = b.b

select count(*)
from a
join b 
  on a.c = b.c

select count(*)
from a
join b 
  on a.b = b.c

set statistics time off
set statistics io off

outputs
    SQL Server parse and compile time: 
   CPU time = 0 ms, elapsed time = 0 ms.

 SQL Server Execution Times:
   CPU time = 0 ms,  elapsed time = 0 ms.
SQL Server parse and compile time: 
   CPU time = 360 ms, elapsed time = 360 ms.

 SQL Server Execution Times:
   CPU time = 0 ms,  elapsed time = 0 ms.

 SQL Server Execution Times:
   CPU time = 0 ms,  elapsed time = 0 ms.

(1 row affected)
Table 'a'. Scan count 9, logical reads 4125, physical reads 0, page server reads 0, read-ahead reads 3510, page server read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob page server reads 0, lob read-ahead reads 0, lob page server read-ahead reads 0.
Table 'b'. Scan count 9, logical reads 4125, physical reads 0, page server reads 0, read-ahead reads 2656, page server read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob page server reads 0, lob read-ahead reads 0, lob page server read-ahead reads 0.
Table 'Worktable'. Scan count 0, logical reads 0, physical reads 0, page server reads 0, read-ahead reads 0, page server read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob page server reads 0, lob read-ahead reads 0, lob page server read-ahead reads 0.

(1 row affected)

 SQL Server Execution Times:
   CPU time = 268 ms,  elapsed time = 117 ms.

(1 row affected)
Table 'a'. Scan count 9, logical reads 4125, physical reads 0, page server reads 0, read-ahead reads 0, page server read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob page server reads 0, lob read-ahead reads 0, lob page server read-ahead reads 0.
Table 'b'. Scan count 9, logical reads 4125, physical reads 0, page server reads 0, read-ahead reads 0, page server read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob page server reads 0, lob read-ahead reads 0, lob page server read-ahead reads 0.
Table 'Worktable'. Scan count 0, logical reads 0, physical reads 0, page server reads 0, read-ahead reads 0, page server read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob page server reads 0, lob read-ahead reads 0, lob page server read-ahead reads 0.

(1 row affected)

 SQL Server Execution Times:
   CPU time = 297 ms,  elapsed time = 184 ms.

(1 row affected)
Table 'a'. Scan count 9, logical reads 4125, physical reads 0, page server reads 0, read-ahead reads 0, page server read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob page server reads 0, lob read-ahead reads 0, lob page server read-ahead reads 0.
Table 'b'. Scan count 9, logical reads 4125, physical reads 0, page server reads 0, read-ahead reads 0, page server read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob page server reads 0, lob read-ahead reads 0, lob page server read-ahead reads 0.
Table 'Worktable'. Scan count 0, logical reads 0, physical reads 0, page server reads 0, read-ahead reads 0, page server read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob page server reads 0, lob read-ahead reads 0, lob page server read-ahead reads 0.

(1 row affected)

 SQL Server Execution Times:
   CPU time = 280 ms,  elapsed time = 111 ms.

Completion time: 2020-10-17T09:56:35.6734439-05:00