I tried it (not court ordered, voluntarily) with ex, at my initiation. I even paid for his account.
My motivation was to limit the amount of contact between us. I found he, and his new wife (OW, my former best friend) were e-mailing me several times a day, and I hoped OFW would curtail that.
It totally backfired.
In addition to sending me the same number of e-mails (just through OFW), they used the "journal" function to "document" every. single. little. thing. Things the kids said, every single item sent between houses, every activity they did, and so forth.
Even when I set it to only receive the once a day 5pm notifications, I had to wade through 7-8 useless/unnecessary communication just to see if there was anything I actually needed to know.
I tried it for 2 months and then told ex I was no longer accessing it and he would have to contact me via e-mail again. They still e-mail me about 4-5x as much as I contact them, but it's much more reasonable than what I was receiving with OFW.