Should dry tortellini be cooked before adding to another recipe?

It depends on what you are making and how much liquid there is. 

If you are adding the tortellini to a soup you can add them as is and they will cook in the broth. The broth will get starchier so if that is not something you want then cook first. 

In most cases cook the tortellini but under cook a bit then add it to your recipe and it will finish cooking.

Yes, cook the tortellini before adding it to another recipe 

Yes. Don't overcook, but slightly under.

Probably yes but not always.  You didn't bother to tell us what you're making and we're not clairvoyant.

If you're making a cold pasta salad, yes, you would want to cook it before adding it.

If you're adding it to a clear broth soup, you probably just cook it in the broth.

Any properly written recipe should tell you how to prepare your ingredients.  Often these preparations are in the ingredients list, not in the paragraph of written-out instructions.

Example:

1 c. CHOPPED onion

1/2 c. GRATED parmesan reggiano

1/4 cup cream

3T flour

2 c. COOKED tortellini

If it doesn't say that it's chopped, grated, cooked, minced, whipped, melted, heated, sifted or whatever, it isn't.