I would strongly recommend against it. A quick Google search said that degus are diurnal, while rats are typically nocturnal. And degus are incredibly social, just like rats, however the two speak different "languages." Living together would be beyond frustrating as they would not be able to effectively communicate with one another. Imagine living in a room with a person from a different country with different values, cultural norms, and they speak different language. That's what it'd feel like to be that degu or that rat.
And if we're bringing diet into this, a degu would not fare well on a rat's diet and vice versa.
I have my sweet, sweet male rats too. They would never hurt anything around me. They want to kiss me all day, crawl around with me, and nap in my arms, but the moment my bird lands on their cage (despite being discouraged from doing that), they will go after him. Bite his toes, his tail feathers, anything and everything.
If you ever worry about different species eating each other, just don't do it. Better safe than sorry.