Hi Lisa!
Anything is possible, but you will certainly be cutting it close. I'd hate to tell you not and miss your only opportunity to dine at Be Our Guest, so I have a couple of suggestions. To be on the complete safe side, have lunch at Be Our Guest instead of dinner. Since it is a quick service restaurant during the day, you can just walk up and in. That way, you'll still have the experience of dining in the castle.
If your hear it set on dinner, totally understandable,
review the menu ahead of time and be ready to order. You certainly don't want to rush your meal here, so placing your order right away will give you more time to enjoy the food and explore the restaurant. After you order, walk around and check everything out. Be sure to visit the West Wing. I would say skip dessert since you will be getting lots of yummy treats during your Pirate and Pals experience, but Be Our Guest is home to my favorite cupcake, the strawberry cream cheese cupcake. If you're up for it, get it. You won't regret it.
When you are finished with your meal, you can opt to take the resort monorail to the Contemporary or walk it. It's a close walk, so I would choose to do that unless you can grab a resort monorail without waiting too long. You are asked to check-in 10 minutes prior, so you don't have to be there terribly early.
Sounds like you will have an amazing evening!
Have a magical day!
Leslie