I think the Democratic leadership’s reaction to these accusations is arguably more important than Franken’s.
If the Senate only conducted an ethics investigation because he gave his blessing to do so then it would send the message that it’s up to the person being accused of misconduct to determine how to proceed.
On the other hand if the Democratic leadership makes it clear that this is NOT something they will tolerate even from a loyal and valued member of their own party then it puts more public pressure on the Republicans to hold themselves to a similar standard of accountability.