Oh, I most certainly would! What you have to remember is your database is your data store, it is not just the data store for the frontend. This is subtle difference, but it's important when you start to consider the future. Right now, you (presumably) own the management applications, but who is to say that in the future this will still be the case?
By off loading as much validation as you can onto the database, you somewhat future proof your application - at least if someone else tries to develop against your database, more of your assumptions will hold.
The drawbacks of having this on the database side is slower insertion, so you need to weigh up how heavy your application is against reading and writing. At work, we have much more demand for read than write, so referential integrity seems obvious. However, our tables are big (and freely available for importing), so we go down a multiple step import route of creating the tables, inserting the data, creating indexes, and then creating foreign keys and other constraints.
I hope this helps!