A better way of asking: Can it be spiritual to have fun?
It can definitely be a bad thing to have fun, if what excites you is perverted or evil.
God gave us joy, and children who learn through playing, and various social connections to enjoy. So yes, I think God wants us to have fun, in a full sense. Not in an empty, mindless entertainment, sense.
The caution is still entertainment. Do you love God with your entire mind? What happens inside your head when you watch a movie, or that favourite TV show, or when you spend time on your hobbies. Those things may, or may not, be good or bad, but if you fail to consider your saviour during the distraction, then your use of them is bad.
Fun must be centered in God, and He must be thanked for every moment of joy that He grants us. And He grants us much. Chiefly in, and through, His son Jesus.