I don't recall any story about Disneyland reaching capacity last year. If you can find that story that might help.
I'd expect it to be very crowded that day, since it falls on a Monday during peak summer season. Many annual passholders who are big Disney fans drop in just for the anniversary. Finally, the
D23 Convention will have just wrapped up, so many Disney fans will already be in town and probably come to the park that day. On the other hand, the park's 60th Anniversary Celebration festivities continued through last year, and that is done with this year. I'm sure it was a big factor last year.
I don't have any guesses about possible closures, since I wasn't aware of this happening last year, but I would definitely plan to enter the park no later than 9:00am, since you're making a special trip. I would not stand in line to purchase tickets. If you must wait until you arrive to buy tickets, I would buy them in the Disneyland app and scan your phone for admission.
Have a great trip! And happy birthday to you daughter!
P.S. Here is a link to Touring Plans' wait times from last year. This will help you gauge how long the waits were for attractions throughout the day, and might answer your question too.
https://touringplans.com/disneyland/wait-times/date/2016-07-17#