The number of login IDs will not have any real impact on performance. You'll likely end up with other issues -- managing all the logins, keeping the passwords secure etc.
What will impact performance is having increased non-pooled connections to the database. Each connection will eat a small amount of RAM on the database server.
Finally, most applications do audit tracking at the application level, not at the database level. You'll need to make sure the database login is preserved throughout the application lifecycle (e.g. what happens if you do a restore?)