Your therapist is being paid. It's not a coffee date. It's not your job to be entertaining. The important thing is being able to use the sessions for therapeutic benefit, not having pleasant conversation. If having your therapist read the letter would help therapy be more beneficial for you, go for it.

I regularly (like every week or two) have my therapist read several written pages, college ruled paper with fairly small handwriting.
It's been really helpful because it gets the topic and things I need to say out there when I struggle to actually say them. After a few sessions in which I didn't do that and had a much harder time talking he actually suggested it as something I could do again because it had been helpful.

It helps him when I actually tell him what's going on. And letters are the way I'm able to do that.
Your therapist should want to help you, and any good therapist would be glad if there's something like writing a letter that will help them help you better.