The frozen spinach is full of water and it takes quite a bit to dry it off--frozen is better used in things like spinach dip or casserole type things. I think you will like the dish much better if you just buy a bag of baby spinach (already washed). I have not used frozen pasta so I don't know what the package says but it might say to cook from frozen. Be sure to save some of the pasta cooking liquid--do not drain it all ( i just scoop out a cup or so before I drain it). You might need to add it in at the end of the dish to make it more saucy . I only see a problem with getting the spinach dry enough plus I think frozen sometimes has an off taste. Yes, small chunks with the hot pasta and as it melts it will form a sauce. Add back little by little some of the reserved pasta water until it is the desired consistency. Be sure to post a photo!
I use melted goat cheese as a sauce for sauteed chicken breasts. It is so tangy and versatile.